COMPOUND ANGLE FORMULA TO EVALUATE THE TRIGONOMETRIC FUNCTIONS WORKSHEET

Simplify each of the following expressions.

Problem 1 :

sin (π  - x)

Solution

Problem 2 :

cos x + 3𝜋2

Solution

Problem 3 :

cos x - 𝜋2

Solution

Problem 4 :

sin (π  + x)

Solution

Problem 5 :

sin (60º - θ) + sin (60º + θ) 

Solution

Problem 6 :

cos (60º - θ) + cos (60º + θ) 

Solution

Problem 7 :

cos x - 𝜋4 + cos x + 𝜋4

Solution

Problem 8 :

sin x + 𝜋6 + sin x - 𝜋6

Solution

Problem 9 :

sin (θ - 180º) + sin (θ + 180º)

Solution

Problem 10 :

cos (90º + θ) + cos (90º - θ)

Solution

Answer Key

1)  sin (π - x) = sin x

2)  cos (x + 3𝜋/2) = sin x

3)  cos (x - 𝜋/2) = sin x

4)  sin (π + x) = -sin x

5)  sin (60º - θ) + sin (60º + θ)  = √3 cos θ

6)  cos (60º - θ) + cos (60º + θ)  = cos θ

7)  cos (x - 𝜋/4) + cos (x + 𝜋/4) = 2 cos x

8)  sin (x + 𝜋/6) + sin (x - 𝜋/6) = 3 sin x

9)  sin (θ - 180º) + sin (θ + 180º)  = -2 sin θ

10)  cos (90º + θ) + cos (90º - θ)  = 0

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