THINKING: 17 marks
[6 marks]
1. Prove the following identities:
a)
tan x  cot x 
1
cos x sin x
b)
sin  x  y 
 1  tan y cot x
sin x cos y
2. Determine all the solutions for the following trigonometric equations:
a) sin 2 x  sin x  2 , exact radian value(s)
[0,2π]
[3 marks]
b) 2 sec 2 x  3  tan x  0 ,rounded to 2 decimal places
5
[3 marks]
1. A softball pitcher winds up and spins her arm around before releasing the ball. The pitcher’s
shoulders are 1.35 m tall and arm is 0.36 m long. The pitcher can spin her arm 15 revolutions every
2 seconds and at t = 0 her hand is it its maximum height.
[5 marks]
a) Determine a sinusoidal equation to represent the height of the pitcher's hand.
b) Determine the height of the pitcher's hand at t = 0.1 seconds.
6
Equivalent Trig Identities
Double Angle Formulas
Compound Angle Formulas
7