Topic 2 Periodic Functions and Applications I
trigonometry – definition and practical applications of the sin, cos and tan ratios simple practical applications of the sine and cosine rules
Model Calculate the value of the pronumeral in each of the following: cos x = x = cos = 50 50’ X° 19 cm 12 cm
Page 33 Exercise 2.1
Find the perimeter of the figure below.
Perimeter = = 221m
Page 36 Exercise 2.2 No. 1 – 6 Page 42 Exercise 2.4 No. 1, 3, Worked solution Ex 2.4 No. 6
The Sine Rule A a b B c C
Model Find x in the following 85 c = x 65 A B C b = 15
Example 11, page 46 (Modelling and Problem Solving) Jermaine sees the top of a sand dune at an angle of 16°. On walking 40m closer, she finds the angle of elevation increases to 22°. What is the height of the sand dune? 16°22° 40m h A C B D * If we knew the length of line DB, we could easily work out the height.
16°22° 40m h A C B D Consider triangle ABD 16° 6°6° 158° 40m d b a
16°22°A B D C h 105.5m
Page 46 Exercise 2.5 N0. 1, 2(b,c,d,e), 3, 4, 7-9
The Cosine Rule A a b B c C Similarly
Model Find the length of the unknown side in the triangle below: A B C c = b= a
Model Find the size of the largest angle in the triangle below: A B C c = b= a=8 N.B. Largest angle is always opposite the largest side
Page 50 Exercise 2.6
Examples 15 & 16, page 51 & 52 Page 53 Exercise 2.7 No. 1(a,b,c,f), 2(a,b,c,f), 4, 7, Worked solution Ex 2.7 No. 13
3D Applications Example 17: page 56 - From point A, a mountain point due north is at an elevation of 20°. From point B, 2Km east of A and on the same level as A, the bearing of the peak is N40°W. Find the height of the peak above A and B.
Consider triangle ABM Angle BAM is a right angle
- From point A, a mountain point due north is at an elevation of 20°. From point B, 2Km east of A and on the same level as A, the bearing of the peak is N40°W. Find the height of the peak above A and B. Consider triangle ABM A M B 50° 2 Km Side AM, which is common to both triangles, can now be calculated
- From point A, a mountain point due north is at an elevation of 20°. From point B, 2Km east of A and on the same level as A, the bearing of the peak is N40°W. Find the height of the peak above A and B. Now consider triangle AMP A P M 20° 2 tan50
Example 18: page 57 John observes that the top of a transmission tower at bearing 038° is at an elevation of 12°. Mary is 575m due east of John and can see the tower on a bearing of 295°. What is the height of the tower?
Example 18: page 57 John observes that the top of a transmission tower at bearing 038° is at an elevation of 12°. Mary is 575m due east of John and can see the tower on a bearing of 295°. What is the height of the tower? 52° 25° 103° FH W 575m We need side WH (f) f w =
Example 18: page 57 John observes that the top of a transmission tower at bearing 038° is at an elevation of 12°. Mary is 575m due east of John and can see the tower on a bearing of 295°. What is the height of the tower? 12° T HW 249.4m We can now calculate tower height
Page 59 Exercise 2.8 Worked solution Ex 2.7 No. 13