1. We are learning to: - Finding connections between different words. (Which PLT skills?) -Accurately finding trigonometric ratios of angles between 0°to 360. (Grade A*) Always aim high! LESSON OBJECTIVES Effective Participator Self Manager Independent Enquirer Creative Thinker Team Worker Reflective Learner PLT Skills Which ones are you using? AUTHOR Where are we in our journey? Real life cross/curricular links? www.mistrymaths.co.uk

2. BRAIN IN GEAR Effective Participator Self Manager Independent Enquirer Creative Thinker Team Worker Reflective Learner Which ones are you using?PLT Skills Work out the following Mathematical anagrams: TASK EXTENSION Develop your own Mathematical anagrams as above as a creative thinker. LICCCY REMMYYST TAQDURAN EXAMPLE DITDIONA can be rearranged to make ADDITION Cyclic Symmetry Quadrant

3. STARTER Effective Participator Self Manager Independent Enquirer Creative Thinker Team Worker Reflective Learner Which ones are you using?PLT Skills TASK 1) 2) 3) Find the area of:Write 8600000 in standard form = 7 10 = x 10 8cm 6cm 7cm 5cm 3x + 6 4x - 5 2x + 8 x + 11 Work out x: Area of a triangle = 8 x 5 2 Area of a triangle = 20cm 2 8.6 6 3x + 6 + 2x + 8 + 4x - 5 + x + 11 = 360 10x 4m 8m 9m x + 20 = 360 - 20 10x = 340° ÷ 10 x = 34° Power 4) 5) Value of: 3 2 25 Work out x: = 1 110° 120° 118° 93° x - Pentagon adds to 540° x = 540° - 120° - 110° - 118° - 93° x =99° Root Reciprocal 25 ( ) 3 = 1 5 3 = 1 125 EXTENSION 4m 8m 7m 5m x Work out x: x 8 = 9 4 x = 9 4 x 8 x =18m

4. Effective Participator Self Manager Independent Enquirer Creative Thinker Team Worker Reflective Learner PLT Skills Which ones are you using? TRIGONOMETRIC ANGLES INTRODUCTION – SINE CURVE x 0°30°45°60°90°120°135°150°180°210°225°240°270°300°315°330°360° y = sin x 00.50.710.871 0.710.50-0.5-0.71-0.87-0.87-0.71-0.50 sin x is positive in the first quadrant sin x is positive in the second quadrant sin x is negative in the third quadrant sin x is negative in the fourth quadrant

5. x 0°30°45°60°90°120°135°150°180°210°225°240°270°300°315°330°360° y = cos x10.870.710.50-0.5-0.71-0.87-0.87-0.71-0.5000.50.710.871 Effective Participator Self Manager Independent Enquirer Creative Thinker Team Worker Reflective Learner PLT Skills Which ones are you using? TRIGONOMETRIC ANGLES INTRODUCTION – COSINE CURVE cos x is positive in the first quadrant cos x is negative in the second quadrant cos x is negative in the third quadrant cos x is positive in the fourth quadrant

6. Effective Participator Self Manager Independent Enquirer Creative Thinker Team Worker Reflective Learner PLT Skills Which ones are you using? TRIGONOMETRIC ANGLES INTRODUCTION – TANGENT CURVE x 0°30°45°60°90°120°135°150°180° y = tan x00.5811.73∞-1.73-0.580 tan x is positive in the first quadrant tan x is negative in the second quadrant tan x is positive in the third quadrant tan x is negative in the fourth quadrant

7. Effective Participator Self Manager Independent Enquirer Creative Thinker Team Worker Reflective Learner PLT Skills Which ones are you using? TRIGONOMETRIC ANGLES SINE CURVE – TRIGONOMETRIC ANGLES For which angles does sin x = 0.5? 30° 150° 30° and 150°

8. Effective Participator Self Manager Independent Enquirer Creative Thinker Team Worker Reflective Learner PLT Skills Which ones are you using? TRIGONOMETRIC ANGLES SINE CURVE – TRIGONOMETRIC ANGLES For which angles does sin x = -0.5? 210° 330 ° 210° and 330°

9. Effective Participator Self Manager Independent Enquirer Creative Thinker Team Worker Reflective Learner PLT Skills Which ones are you using? TRIGONOMETRIC ANGLES COSINE CURVE – TRIGONOMETRIC ANGLES For which angles does cos x = 0.5? 60° 300° 60° and 300°

10. Effective Participator Self Manager Independent Enquirer Creative Thinker Team Worker Reflective Learner PLT Skills Which ones are you using? TRIGONOMETRIC ANGLES COSINE CURVE – TRIGONOMETRIC ANGLES For which angles does cos x = -0.5? 120° 240 ° 120° and 240°

11. Effective Participator Self Manager Independent Enquirer Creative Thinker Team Worker Reflective Learner PLT Skills Which ones are you using? TRIGONOMETRIC ANGLES TANGENT CURVE – TRIGONOMETRIC ANGLES For which angles does tan x = 1? 45° 225° 45° and 225°

12. Effective Participator Self Manager Independent Enquirer Creative Thinker Team Worker Reflective Learner PLT Skills Which ones are you using? TRIGONOMETRIC ANGLES TANGENT CURVE – TRIGONOMETRIC ANGLES For which angles does tan x = -1? -45° 135 ° -45° and 135°

13. Effective Participator Self Manager Independent Enquirer Creative Thinker Team Worker Reflective Learner PLT Skills Which ones are you using? TRIGONOMETRIC CURVES Cyclic → Repeat their pattern indefinitely in both directions Every value of sine between -1 and 1 gives two angles between 0° and 360° When the value of sine is positive, both angles are between 0° and 180° When the value of sine is negative, both angles are between 0° and 180° Cyclic → Repeat their pattern indefinitely in both directions Every value of cosine between -1 and 1 gives two angles between 0° and 360° When the value of cosine is positive, one angle is between 0° and 90° and the other is between 270° and 360° When the value of cosine is negative, both angles are between 90° and 270° Every value of tangent between -1 and 1 gives two angles between 0° and 360° When the value of tangent is positive, one angle is between 0° and 90° and the other is between 180° and 270° When the value of tangent is negative, one angle is between -90° and 0° and the other is between 90° and 180°

14. Effective Participator Self Manager Independent Enquirer Creative Thinker Team Worker Reflective Learner PLT Skills Which ones are you using? TRIGONOMETRIC ANGLES CAST DIAGRAM 0° 90° 180° 270° / 360° C os (+) A ll (+) S in (+) T an (+) All of sin θ, cos θ and tan θ are positive in this quadrant CAST Only cos θ is positive in this quadrant Only sin θ is positive in this quadrant Only tan θ is positive in this quadrant Quadrant 1 Quadrant 2 Quadrant 3 Quadrant 4

15. Effective Participator Self Manager Independent Enquirer Creative Thinker Team Worker Reflective Learner PLT Skills Which ones are you using? TRIGONOMETRIC ANGLES 0° 90° 180° 270° / 360° C os (+) A ll (+) S in (+) T an (+) All of sin θ, cos θ and tan θ are positive in this quadrant CAST Only cos θ is positive in this quadrant Only tan θ is positive in this quadrant 30° sin θ cos θ y x 150° sin θ -cos θ y -x -sin θ -y 210° 330° -sin θ -y-y sin 30° = ……………. sin 150° sin 210° = ……………. sin 330° cos 30° = ……………. cos 330° cos 150° = ……………. cos 210° tan 30° = ……………. tan 210° tan 150° = ……………. tan 330° Only sin θ is positive in this quadrant

16. Effective Participator Self Manager Independent Enquirer Creative Thinker Team Worker Reflective Learner PLT Skills Which ones are you using? TRIGONOMETRIC ANGLES EXAMPLES – SIN θ 1) Find the other angle which has the same value as sin 60° 2) Find the other angle which has the same value as sin 225° 60° 120° sin 120° 225° 315° sin 315° Reflection in the y-axis

17. Effective Participator Self Manager Independent Enquirer Creative Thinker Team Worker Reflective Learner PLT Skills Which ones are you using? TRIGONOMETRIC ANGLES EXAMPLES – COS θ 1) Find the other angle which has the same value as cos 60° 2) Find the other angle which has the same value as cos 225° 60° 300° cos 300° 225° 135° cos 135° Reflection in the x-axis

18. Effective Participator Self Manager Independent Enquirer Creative Thinker Team Worker Reflective Learner PLT Skills Which ones are you using? TRIGONOMETRIC ANGLES EXAMPLES – TAN θ 1) Find the other angle which has the same value as tan 60° 2) Find the other angle which has the same value as tan 225° 60° 240° tan 240° 315° 135° tan 315° Makes a diagonal line

19. Effective Participator Self Manager Independent Enquirer Creative Thinker Team Worker Reflective Learner PLT Skills Which ones are you using? TRIGONOMETRIC ANGLES TASK 1 (GRADE A*) – SIN θ 1) Find the other angle which has the same value for the following: (a) sin 45° (b) sin 80° (c) sin 25° (d) sin 160° (e) sin 190° (f) sin 280° 45° 135° sin 135° 80° 100° sin 100° 25°155° sin 155° 160° 20° sin 20° 190° 350° sin 350° 280° 260° sin 260°

20. Effective Participator Self Manager Independent Enquirer Creative Thinker Team Worker Reflective Learner PLT Skills Which ones are you using? TRIGONOMETRIC ANGLES TASK 2 (GRADE A*) – COS θ 1) Find the other angle which has the same value for the following: (a) cos 45° (b) cos 80° (c) cos 25° (d) cos 160° (e) cos 190° (f) cos 260° 45° 315° cos 315° 80° 280° cos 280° 25° 335° cos 335° 160° 200° cos 200° 190° 170° cos 170° 100° 260° cos 100°

21. Effective Participator Self Manager Independent Enquirer Creative Thinker Team Worker Reflective Learner PLT Skills Which ones are you using? TRIGONOMETRIC ANGLES TASK 3 (GRADE A*) – TAN θ 1) Find the other angle which has the same value for the following: (a) tan 45° (b) tan 80° (c) tan 25° (d) tan 160° (e) tan 190° (f) tan 280° 45° 225° tan 225° 80° 260° tan 260° 25° 205° tan 205° 160° 340° tan 340° 190° 10° tan 10° 280° 100° tan 100°

22. Effective Participator Self Manager Independent Enquirer Creative Thinker Team Worker Reflective Learner PLT Skills Which ones are you using? TRIGONOMETRIC ANGLES TASK 4 (GRADE A*) – MIXTURE OF SIN θ, COS θ & TAN θ 1) Find the other angle which has the same value for the following: (a) sin 35° (b) cos 65° (c) tan 55° (d) cos 75° (e) tan 75° (f) sin 15° 35° 145° sin 145° 65° 295° cos 295° 55° 235° tan 235° 75° 255° cos 255° 255° 75° tan 255° 165° 15° sin 345°

23. Effective Participator Self Manager Independent Enquirer Creative Thinker Team Worker Reflective Learner PLT Skills Which ones are you using? TRIGONOMETRIC ANGLES TASK 4 (GRADE A*) – MIXTURE OF SIN θ, COS θ & TAN θ 2) Find the other angle which has the same value for the following: (a) sin 115° (b) cos 125° (c) tan 140° (d) cos 165° (e) tan 175° (f) sin 130° 115° 65° sin 65° 125° 235° cos 235° 140° 320° tan 320° 165° 195° cos 195° 175° 355° tan 355° 50° 130° sin 50°

24. Effective Participator Self Manager Independent Enquirer Creative Thinker Team Worker Reflective Learner PLT Skills Which ones are you using? TRIGONOMETRIC ANGLES TASK 4 (GRADE A*) – MIXTURE OF SIN θ, COS θ & TAN θ 3) Find the other angle which has the same value for the following: (a) sin 200° (b) cos 260° (c) tan 265° (d) cos 195° (e) tan 185° (f) sin 215° 200° 340° sin 340° 260° 100° cos 100° 265° 85°c tan 85° 195° 165° cos 165° 185° 5° tan 5° 215° 325° sin 325°

25. Effective Participator Self Manager Independent Enquirer Creative Thinker Team Worker Reflective Learner PLT Skills Which ones are you using? TRIGONOMETRIC ANGLES TASK 4 (GRADE A*) – MIXTURE OF SIN θ, COS θ & TAN θ 4) Find the other angle which has the same value for the following: (a) sin 290° (b) cos 280° (c) tan 350° (d) cos 295° (e) tan 310° (f) sin 345° 290° 250° sin 250° 280° 80° cos 80° 350° 170° tan 170° 295° 65° cos 65° 130° 310° tan 130° 345° 195° sin 195°

26. Effective Participator Self Manager Independent Enquirer Creative Thinker Team Worker Reflective Learner PLT Skills Which ones are you using? TRIGONOMETRIC ANGLES EXTENSION 1 (GRADE A*) – WITHOUT A CAST DIAGRAM 1) Find the other angle which has the same value for the following: (a) sin 50° (b) cos 40° (c) tan 80° sin 130° cos 320° tan 260° (c) cos 130° (d) tan 170° (e) sin 120° cos 230° tan 350° sin 60° (f) tan 55° (g) sin 125° (h) cos 185° tan 235° sin 55° cos 175° (i) sin 280° (j) tan 170° (k) sin 75° sin 260° tan 350° sin 105° (l) sin 48° (m) cos 69° (n) tan 19° sin 132° cos 291° tan 199° (o) cos 217° (p) tan 284° (q) sin 136° cos 143° tan 104° sin 44° (r) tan 312° (s) cos 179° (t) sin 12° tan 132° cos 181° sin 168° (u) sin 359° (v) cos 115° (w) tan 203° sin 181° cos 245° tan 23° (x) cos 301° (y) tan 201° (z) sin 1° cos 59° tan 21° sin 179°

27. Effective Participator Self Manager Independent Enquirer Creative Thinker Team Worker Reflective Learner PLT Skills Which ones are you using? TRIGONOMETRIC ANGLES EXAMPLES 2 – SIN θ 1) Find the angles with a sine of 0.52 2) Find the angles with a sine of -0.256 sin 0.52 = 31.3° 148.7° 31.3° and 148.7° sin -0.236 =-14.8° 345.2° 194.8° 194.8° and 345.2° Reflection in the y-axis

28. Effective Participator Self Manager Independent Enquirer Creative Thinker Team Worker Reflective Learner PLT Skills Which ones are you using? TRIGONOMETRIC ANGLES EXAMPLES 2 – COS θ 1) Find the angles with a cosine of 0.68 2) Find the angles with a cosine of -0.372 cos 0.68 = 47.2° 312.8° 47.2° and 312.8° cos -0.372 =111.8° 248.2° 111.8° and 248.2° Reflection in the x-axis

29. Effective Participator Self Manager Independent Enquirer Creative Thinker Team Worker Reflective Learner PLT Skills Which ones are you using? TRIGONOMETRIC ANGLES EXAMPLES 2 – TAN θ 1) Find the angles with a tangent of 0.715 2) Find the angles with a tangent of -1.2 tan 0.715 = 35.6° 215.6° 35.6° and 215.6° tan -1.2 =-50.2° 309.8° 129.8° 129.8° and 309.8° Makes a diagonal line

30. Effective Participator Self Manager Independent Enquirer Creative Thinker Team Worker Reflective Learner PLT Skills Which ones are you using? TRIGONOMETRIC ANGLES TASK 5 (GRADE A*) – SIN θ 1) State the two angles between 0° and 360° for each of these sine values: (a) 0.2 (b) 0.7 (c) 0.5 (d) -0.4 (e) -0.55 (f) -0.136 sin 0.2 = 11.5° 168.5° 11.5° and 168.5° 44.4° 135.6° 44.4° and 135.6° 30° 150° 30° and 150° sin 0.7 = sin 0.5 = sin -0.4 = -23.6° 336.4° 203.6° 203.6° and 336.4° sin -0.55 = -33.4° 326.6° 213.4° 213.4° and 326.6° sin -0.136 = -7.8° 352.2° 187.8° 187.8° and 352.2°

31. Effective Participator Self Manager Independent Enquirer Creative Thinker Team Worker Reflective Learner PLT Skills Which ones are you using? TRIGONOMETRIC ANGLES TASK 6 (GRADE A*) – COS θ 1) State the two angles between 0° and 360° for each of these cosine values: (a) 0.4 (b) 0.6 (c) 0.5 (d) -0.1 (e) -0.65 (f) -0.241 cos 0.4 = 66.4° 293.6° 66.4° and 293.6° 53.1° 306.9° 53.1° and 306.9° 60° 300° 60° and 300° cos 0.6 = cos 0.5 = cos -0.1 = 95.7° 264.3° 95.7° and 264.3° cos -0.65 = 130.5° 229.5° 130.5° and 229.5° cos -0.241 = 103.9° 256.1° 103.9° and 256.1°

32. Effective Participator Self Manager Independent Enquirer Creative Thinker Team Worker Reflective Learner PLT Skills Which ones are you using? TRIGONOMETRIC ANGLES TASK 7 (GRADE A*) – TAN θ 1) State the two angles between 0° and 360° for each of these tangent values: (a) 0.8 (b) 0.1 (c) 0.3 (d) -0.9 (e) -0.35 (f) -0.682 tan 0.8 = 38.7° 218.7° 38.7° and 218.7° 5.7° 185.7° 5.7° and 185.7° 16.7° 196.7° 16.7° and 196.7° tan 0.1 = tan 0.3 = tan -0.9 = -42.0° 318° 138° 138° and 318° tan -0.35 = -19.3° 340.7° 160.7° 160.7° and 340.7° tan -0.682 = -34.3° 325.7° 145.7° 145.7° and 325.7°

33. Effective Participator Self Manager Independent Enquirer Creative Thinker Team Worker Reflective Learner PLT Skills Which ones are you using? TRIGONOMETRIC ANGLES TASK 8 (GRADE A*) – MIXTURE OF SIN θ, COS θ & TAN θ 1) (a) sine of 0.1 (b) cosine of 0.8 (c) tangent of 0.5 (d) cosine of 0.6 (e) tangent of 0.4 (f) sine of 0.9 State the two angles between 0° and 360° for each of these values: sin 0.1 = 5.7° 174.3° 5.7° and 174.3° cos 0.8 = 36.9° 323.1° 36.9° and 323.1° tan 0.5 = 26.6° 206.6° 26.6° and 206.6° cos 0.6 = 53.1° 306.9° 53.1° and 306.9° tan 0.4 = 21.8° 201.8° 21.8° and 201.8° sin 0.9 = 64.2° 115.8° 64.2° and 115.8°

34. Effective Participator Self Manager Independent Enquirer Creative Thinker Team Worker Reflective Learner PLT Skills Which ones are you using? TRIGONOMETRIC ANGLES TASK 8 (GRADE A*) – MIXTURE OF SIN θ, COS θ & TAN θ 2) (a) sine of 0.27 (b) cosine of 0.62 (c) tangent of 0.12 (d) Cosine of 0.86 (e) tangent of 0.75 (f) sine of 0.38 State the two angles between 0° and 360° for each of these values: sin 0.27 = 15.7° 164.3° 15.7° and 164.3° cos 0.62 = 51.7° 308.3° 51.7° and 308.3° tan 0.12 = 6.8° 186.8° 6.8° and 186.8° cos 0.86 = 30.7° 329.3° 30.7° and 329.3° tan 0.75 = 36.9° 216.9° 36.9° and 216.9° sin 0.38 = 22.3° 157.7° 22.3° and 157.7°

35. Effective Participator Self Manager Independent Enquirer Creative Thinker Team Worker Reflective Learner PLT Skills Which ones are you using? TRIGONOMETRIC ANGLES TASK 8 (GRADE A*) – MIXTURE OF SIN θ, COS θ & TAN θ 3) (a) sine of -0.3 (b) cosine of -0.5 (c) tangent of -0.8 (d) cosine of -0.6 (e) tangent of -0.2 (f) sine of -0.4 State the two angles between 0° and 360° for each of these values: sin -0.3 = -17.5° 342.5° 197.5° 197.5° and 342.5° cos -0.5 = 120° 240° 120° and 240° tan -0.8 = -38.7° 321.3° 141.3° 141.3° and 321.3° cos -0.6 = 126.9° 233.1° 126.9° and 233.1° tan -0.2 = -11.3° 348.7° 168.7° 168.7° and 348.7° sin -0.4 = -23.6° 336.4° 203.6° 203.6° and 336.4°

36. Effective Participator Self Manager Independent Enquirer Creative Thinker Team Worker Reflective Learner PLT Skills Which ones are you using? TRIGONOMETRIC ANGLES TASK 8 (GRADE A*) – MIXTURE OF SIN θ, COS θ & TAN θ 4) (a) sine of -0.46 (b) cosine of -0.62 (c) tangent of -0.69 (d) cosine of -0.24 (e) tangent of -0.48 (f) sine of -0.84 State the two angles between 0° and 360° for each of these values: sin -0.46 = 27.4° 152.6° 27.4° and 152.6° cos -0.62 = 128.3° 231.7° 128.3° and 231.7° tan -0.69 = -34.6° 325.4° 145.4° 145.4° and 325.4° cos -0.24 = 103.9° 256.1° 103.9° and 256.1° tan -0.48 = -25.6° 334.4° 154.4° 154.4° and 334.4° sin -0.84 = -57.1° 302.9° 237.1° 237.1° and 302.9°

37. Effective Participator Self Manager Independent Enquirer Creative Thinker Team Worker Reflective Learner PLT Skills Which ones are you using? TRIGONOMETRIC ANGLES EXTENSION 2 (GRADE A*) – WITHOUT A CAST DIAGRAM 1) (a) sine of 0.5 (b) cosine of 0.2 (c) tangent of 0.7 30° & 150° 78.5° & 281.5° 35° & 215° (d) cosine of 0.8 (e) tangent of 0.5 (f) sine of 0.1 36.9° & 323.1° 26.6° & 206.6° 5.7° & 174.3° (g) tangent of 0.12 (h) sine of 0.83 (i) cosine of 0.91 6.8° & 186.8° 56.1° & 123.9° 24.5° & 335.5° (j) sine of 0.47 (k) tangent of 0.22 (l) sine of 0.72 28° & 152° 12.4° & 192.4° 46.1° & 133.9° (m) sine of 0.462 (n) cosine of 0.673 (o) tangent of 0.836 27.5° & 152.5° 47.7° & 312.3°39.9° & 219.9° (p) cosine of -0.6 (q) tangent of -0.4 (r) sine of -0.8 126.9° & 233.1° 158.2° & 338.2° 233.1° & 306.9° (s) tangent of -0.3 (t) cosine of -0.9 (u) sine of -0.5 163.3° & 343.3°154.2° & 205.8° 210° & 330° (v) sine of -0.63 (w) cosine of -0.26 (x) tangent of -0.94 219.1° & 320.9° 105.1° & 254.9° 136.8° & 316.8° (y) cosine of -0.13 (z) tangent of -0.47 ($) sine of -0.71 97.5° & 262.5° 154.8° & 334.8°224.4° & 315.6° State the two angles between 0° and 360° for each of these values:

38. Effective Participator Self Manager Independent Enquirer Creative Thinker Team Worker Reflective Learner PLT Skills Which ones are you using? MINI-PLENARY 1 – ASSESSING UNDERSTANDING A student has been struggling with trigonometric angles. Her answers are shown below. What is she doing wrong and how would you help her? TRIGONOMETRIC ANGLES Find the other angle which has the same value for the following: (a) sin 25° (b) cos 62° (c) tan 50° 25° 335° sin 335° 62° 118° cos 118° 50° 220° tan 230° QUESTION 155° sin 155° (Reflection in y-axis) 298° cos 298° (Reflection in x-axis) 230° cos 230° (Diagonal line)

39. Effective Participator Self Manager Independent Enquirer Creative Thinker Team Worker Reflective Learner PLT Skills Which ones are you using? MINI-PLENARY 2 – ASSESSING UNDERSTANDING A student has been struggling with trigonometric angles. Her answers are shown below. What is she doing wrong and how would you help her? TRIGONOMETRIC ANGLES (a) (c) 53.1° 306.9° 71.3° 198.7° 348.7° QUESTION (a) sine of 0.8 (b) cosine of 0.32 (c) tangent of -0.2 State the two angles between 0° and 360° for each of these values: sin 0.8 = 53.1° cos 0.32 = 71.3° tan -0.2 = -11.3° 126.9° 53.1° & 126.9° (Reflection in y-axis) 288.7° 71.3° & 288.7° (Reflection in x-axis) 168.7° 11.3° 191.3° 168.7° & 348.7° (Diagonal line)

40. DISCOVERY Effective Participator Self Manager Independent Enquirer Creative Thinker Team Worker Reflective Learner Which ones are you using?PLT Skills LINK BACK TO OBJECTIVES - Accurately finding trigonometric ratios of angles between 0°to 360. What grade are we working at?

41. Effective Participator Self Manager Independent Enquirer Creative Thinker Team Worker Reflective Learner PLT Skills Which ones are you using? PLENARY ACTIVITY– PROBLEM SOLVING (GRADE A*) Suppose the sine key on your calculator is broken, but not the cosine key. Show how you could calculate these: TRIGONOMETRIC ANGLES (a) sin 35° (b) sin 150° 35° 55° cos 55° 60° 150° sin θ cos θ Need to make cos θ the same length as sin θ 90° - 35° =55° sin θ -cos θ Need to make cos θ the same length as sin θ 90° - 30° = 60° 30° cos 60°

42. Draw your brain What have you learnt? In your brain, write or draw everything you can remember about finding trigonometric ratios of angles between 0°to 360. It can be a skill or a reflection, or something else that might be prominent in your brain. What grade are we working at? Where are we in our journey?

43. . How well do you understand the task? I don’t understand I nearly understand I fully understand Creative Entrepreneur Responsible Citizen Independent Learner Positive Thinker Team Worker Reflective Learner Enterprise Skills Which ones are you using? SELF ASSESSMENT Plenary Activity www.mistrymaths.co.uk

44. SELF ASSESSMENT Plenary Activity On your post it notes… Think about how you can improve your work. On your post it notes… Think about how you can improve your work. WWW (What Went Well) EBI (Even Better If) Creative Entrepreneur Responsible Citizen Independent Learner Positive Thinker Team Worker Reflective Learner Enterprise Skills Which ones are you using? www.mistrymaths.co.uk

45. Effective Participator Self Manager Independent Enquirer Creative Thinker Team Worker Reflective Learner PLT Skills Which ones are you using? TRIGONOMETRIC ANGLES TASK 1 (GRADE A*) – SIN θ 1) Find the other angle which has the same value for the following: (a) sin 45° (b) sin 80° (c) sin 25° (d) sin 160° (e) sin 190° (f) sin 280°

46. Effective Participator Self Manager Independent Enquirer Creative Thinker Team Worker Reflective Learner PLT Skills Which ones are you using? TRIGONOMETRIC ANGLES TASK 2 (GRADE A*) – COS θ 1) Find the other angle which has the same value for the following: (a) cos 45° (b) cos 80° (c) cos 25° (d) cos 160° (e) cos 190° (f) cos 260°

47. Effective Participator Self Manager Independent Enquirer Creative Thinker Team Worker Reflective Learner PLT Skills Which ones are you using? TRIGONOMETRIC ANGLES TASK 3 (GRADE A*) – TAN θ 1) Find the other angle which has the same value for the following: (a) tan 45° (b) tan 80° (c) tan 25° (d) tan 160° (e) tan 190° (f) tan 280°

48. Effective Participator Self Manager Independent Enquirer Creative Thinker Team Worker Reflective Learner PLT Skills Which ones are you using? TRIGONOMETRIC ANGLES TASK 4 (GRADE A*) – MIXTURE OF SIN θ, COS θ & TAN θ 1) Find the other angle which has the same value for the following: (a) sin 35° (b) cos 65° (c) tan 55° (d) cos 75° (e) tan 75° (f) sin 15°

49. Effective Participator Self Manager Independent Enquirer Creative Thinker Team Worker Reflective Learner PLT Skills Which ones are you using? TRIGONOMETRIC ANGLES TASK 4 (GRADE A*) – MIXTURE OF SIN θ, COS θ & TAN θ 2) Find the other angle which has the same value for the following: (a) sin 115° (b) cos 125° (c) tan 140° (d) cos 165° (e) tan 175° (f) sin 130°

50. Effective Participator Self Manager Independent Enquirer Creative Thinker Team Worker Reflective Learner PLT Skills Which ones are you using? TRIGONOMETRIC ANGLES TASK 4 (GRADE A*) – MIXTURE OF SIN θ, COS θ & TAN θ 3) Find the other angle which has the same value for the following: (a) sin 200° (b) cos 260° (c) tan 265° (d) cos 195° (e) tan 185° (f) sin 215°

51. Effective Participator Self Manager Independent Enquirer Creative Thinker Team Worker Reflective Learner PLT Skills Which ones are you using? TRIGONOMETRIC ANGLES TASK 4 (GRADE A*) – MIXTURE OF SIN θ, COS θ & TAN θ 4) Find the other angle which has the same value for the following: (a) sin 290° (b) cos 280° (c) tan 350° (d) cos 295° (e) tan 310° (f) sin 345°

52. Effective Participator Self Manager Independent Enquirer Creative Thinker Team Worker Reflective Learner PLT Skills Which ones are you using? TRIGONOMETRIC ANGLES EXTENSION 1 (GRADE A*) – WITHOUT A CAST DIAGRAM 1) Find the other angle which has the same value for the following: (a) sin 50° (b) cos 40° (c) tan 80° (c) cos 130° (d) tan 170° (e) sin 120° (f) tan 55° (g) sin 125° (h) cos 185° (i) sin 280° (j) tan 170° (k) sin 75° (l) sin 48° (m) cos 69° (n) tan 19° (o) cos 217° (p) tan 284° (q) sin 136° (r) tan 312° (s) cos 179° (t) sin 12° (u) sin 359° (v) cos 115° (w) tan 203° (x) cos 301° (y) tan 201° (z) sin 1°

53. Effective Participator Self Manager Independent Enquirer Creative Thinker Team Worker Reflective Learner PLT Skills Which ones are you using? TRIGONOMETRIC ANGLES TASK 5 (GRADE A*) – SIN θ 1) State the two angles between 0° and 360° for each of these sine values: (a) 0.2 (b) 0.7 (c) 0.5 (d) -0.4 (e) -0.55 (f) -0.136

54. Effective Participator Self Manager Independent Enquirer Creative Thinker Team Worker Reflective Learner PLT Skills Which ones are you using? TRIGONOMETRIC ANGLES TASK 6 (GRADE A*) – COS θ 1) State the two angles between 0° and 360° for each of these cosine values: (a) 0.4 (b) 0.6 (c) 0.5 (d) -0.1 (e) -0.65 (f) -0.241

55. Effective Participator Self Manager Independent Enquirer Creative Thinker Team Worker Reflective Learner PLT Skills Which ones are you using? TRIGONOMETRIC ANGLES TASK 7 (GRADE A*) – TAN θ 1) State the two angles between 0° and 360° for each of these tangent values: (a) 0.8 (b) 0.1 (c) 0.3 (d) -0.9 (e) -0.35 (f) -0.682

56. Effective Participator Self Manager Independent Enquirer Creative Thinker Team Worker Reflective Learner PLT Skills Which ones are you using? TRIGONOMETRIC ANGLES TASK 8 (GRADE A*) – MIXTURE OF SIN θ, COS θ & TAN θ 1) (a) sine of 0.1 (b) cosine of 0.8 (c) tangent of 0.5 (d) cosine of 0.6 (e) tangent of 0.4 (f) sine of 0.9 State the two angles between 0° and 360° for each of these values:

57. Effective Participator Self Manager Independent Enquirer Creative Thinker Team Worker Reflective Learner PLT Skills Which ones are you using? TRIGONOMETRIC ANGLES TASK 8 (GRADE A*) – MIXTURE OF SIN θ, COS θ & TAN θ 2) (a) sine of 0.27 (b) cosine of 0.62 (c) tangent of 0.12 (d) Cosine of 0.86 (e) tangent of 0.75 (f) sine of 0.38 State the two angles between 0° and 360° for each of these values:

58. Effective Participator Self Manager Independent Enquirer Creative Thinker Team Worker Reflective Learner PLT Skills Which ones are you using? TRIGONOMETRIC ANGLES TASK 8 (GRADE A*) – MIXTURE OF SIN θ, COS θ & TAN θ 3) (a) sine of -0.3 (b) cosine of -0.5 (c) tangent of -0.8 (d) cosine of -0.6 (e) tangent of -0.2 (f) sine of -0.4 State the two angles between 0° and 360° for each of these values:

59. Effective Participator Self Manager Independent Enquirer Creative Thinker Team Worker Reflective Learner PLT Skills Which ones are you using? TRIGONOMETRIC ANGLES TASK 8 (GRADE A*) – MIXTURE OF SIN θ, COS θ & TAN θ 4) (a) sine of -0.46 (b) cosine of -0.62 (c) tangent of -0.69 (d) cosine of -0.24 (e) tangent of -0.48 (f) sine of -0.84 State the two angles between 0° and 360° for each of these values:

60. Effective Participator Self Manager Independent Enquirer Creative Thinker Team Worker Reflective Learner PLT Skills Which ones are you using? TRIGONOMETRIC ANGLES EXTENSION 2 (GRADE A*) – WITHOUT A CAST DIAGRAM 1) (a) sine of 0.5 (b) cosine of 0.2 (c) tangent of 0.7 (c) cosine of 0.8 (d) tangent of 0.5 (e) sine of 0.1 (f) tangent of 0.12 (g) sine of 0.83 (h) cosine of 0.91 (i) sine of 0.47 (j) tangent of 0.22 (k) sine of 0.72 (l) sine of 0.462 (m) cosine of 0.673 (n) tangent of 0.836 (o) cosine of -0.6 (p) tangent of -0.4 (q) sine of -0.8 (r) tangent of -0.3 (s) cosine of -0.9 (t) sine of -0.5 (u) sine of -0.63 (v) cosine of -0.26 (w) tangent of -0.94 (x) cosine of -0.13 (y) tangent of -0.47 (z) sine of -0.71 State the two angles between 0° and 360° for each of these values: