1. Further Trigonometry Graphs and equations

2. Determine the period, max and min of each graph Period = 360  b Amplitude = a Max = a + c Min = c – a Period = 360  b Amplitude = a Max = a + c Min = c – a Period = 180  b Amplitude =  Max =  Min = –  Period = 360  4 = 90  Amplitude = 3 Max = 3 + 1 = 4 Min = 1 – 3 = -2 Period = 360  3 = 120  Amplitude = 5 Max = 5 – 2 = 3 Min = -2 – 5 = -7 Period = 180  3 = 60  Amplitude =  Max =  Min = – 

3. Determine the equation of each graph below x y 180  90  -4 4 x y 45  90  7 -7 Period = 180  Amplitude = 4 Base line = 0 Cosine graph Period = 45  Amplitude = 7 Base line = 0 Sine graph

4. Determine the equation of each graph below x y 120  60  0 4 x y 180  360  3 -7 Period = 120  Amplitude = 2 Base line = +2 Cosine graph Period = 180  Amplitude = 5 Base line = -2 Sine graph

5. Determine the equation of each graph below Period = 180  Amplitude =  Base line = 0 Tan graph Period = 90  Amplitude =  Base line = -3 Tan graph x y 90  270  450  x y 45  135  225  -3

6. Sketch the following graphs for 0  x  360  Period = 360  2 = 180  Amplitude = 6 Period = 360  1 = 180  Amplitude = 5 Max = 5 – 1 = 4 Min = -1 – 5 = -6 Base line = -1 x y 6 -6 180  360  4 -6 180  360  x y

7. Solve the following Trig equations for 0  x  360 AS TC AS TC

8. AS TC AS TC

9. AS TC AS TC

10. Consider the special Triangles and complete the table 1 1 45  22 1 2 60  30  33 45  60  xx

11. Write down the following exact values 30  45  60  xx Sin 150  Tan 315  Cos 300  Tan 690  Sin -90  Sin (180 – 30)  AS TC + Sin 30  1/21/2 Tan (360 – 45)  - Tan 45  Cos (360 – 60)  + Cos 60  1/21/2 Tan 330  - tan 30  - 1 /  3 Tan (360 – 30)  sin 270 

12. Quadratic Equations Parabolas and Graphs

13. Solve each of the following by factorising x 2 – 5x = 0x 2 – 2x – 8 = 0 x 2 = 64 x(x – 5) = 0 x = 0 or x – 5 = 0 x = 0 and x = 5 (x – 4 )(x + 2) = 0 x – 4 = 0 or x + 2 = 0 x = 4 and x = -2 x 2 – 64 = 0 (x – 8 )(x + 8) = 0 x – 8 = 0 or x + 8 = 0 x = 8 and x = -8 x 2 – 16 = 15x (x – 16 )(x + 1) = 0 x – 16 = 0 or x + 1 = 0 x = 16 and x = -1 x 2 – 15x – 16 = 0

14. 2x 2 + 11x + 12 = 0 (2x + 3)(x + 4) = 0 2x x 4 3 x 6 2 x 3 4 Solve each of the following by factorising 3x 2 + 13x = 10 (3x  2)(x + 5) = 0 3x x -5 2 3x x 5 -2 3x x -2 5 3x 2 + 13x – 10 = 0 2x + 3 = 0 or x + 4 = 0 x = - 3 / 2 and x = -4 3x  2 = 0 or x + 5 = 0 x = 2 / 3 and x = -5

15. Solve the correct to 1 d.p. where possible 2x 2  3x  4 = 0 x 2 + 6 = 2x a = 2, b= -3, c = -4 x = 2.4x = -0.9 x 2  2x + 6 = 0 a = 1, b= -2, c = 6

16. Solve the correct to 1 d.p. where possible 3x 2 + 2x  6 = 09  5x  2x 2 = 0 a = 3, b= 2, c = -6 x = 1.1x = -1.8 a = -2, b= -5, c = 9 x = -3.7x = 1.2

17. Given the area of the Rectangle determine x and the dimensions of the shape 2x + 1 x – 2Area = 52 cm 2 (2x + 1)(x – 2) = 52 2x 2 – 4x + x – 2 = 52 2x 2 – 3x – 2 = 52 2x 2 – 3x – 54 = 0 2x x -9 6 2x x 9 -6 (2x + 9)(x – 6) = 0 2x + 9 = 0 or x – 6 = 0 x = - 9 / 2 or x = 6 x = 6 as you can’t have a negative length Dimensions are 13 cm by 4 cm

18. Sketching Parabolas y = ax 2 + bx + c y x b. Y-intercept when x = 0 c. X-intercept (roots) when y = 0 d. Axis of symmetry e. Turning point a. Shape +x 2  -x 2 

19. E.g.1 Sketch y = x 2  2x  8 y x b. Y-intercept when x = 0 c. X-intercept (roots) when y = 0 d. Axis of symmetry e. Turning point a. Shape +x 2  -x 2  y = 0 – 0 – 8(0,–8) -8 x 2 – 2x – 8 = 0 (x – 4)(x + 2) = 0 x = 4 and x = -2 -24 Midpoint of x= -2 and x = 4 (-2+4)  2  x = 1 1 When x = 1 y = (1) 2 – 2(1) – 8 y = 1 – 2 – 8 (1,– 9) (1,-9)

20. E.g.2 Sketch y = 12 + 4x  x 2 y x b. Y-intercept when x = 0 c. X-intercept (roots) when y = 0 d. Axis of symmetry e. Turning point a. Shape +x 2  -x 2  y = 12 + 0 – 0(0,12) 12 12 + 4x  x 2 = 0 (6 – x)(2 + x) = 0 x = 6 and x = -2 -24 Midpoint of x= -2 and x = 6 (-2+6)  2  x = 2 2 When x = 2 y = 12 + 4(2)  (2) 2 y = 12 + 8 – 4 (2,16)