PRACTICE PROBLEMS ON NEGATIVE AND COMPLEMENTARY ANGLES IN TRIGONOMETRY

Simplify:

Problem 1:

sin θ + sin (-θ)

Solution

Problem 2 :

tan (-θ) - tan θ

Solution

Problem 3 :

2 cos θ + cos (-θ)

Solution

Problem 4 :

3 sin θ - sin (-θ)

Solution

Problem 5 :

cos² (-α)

Solution

Problem 6 :

sin² (-α)

Solution

Problem 7 :

cos (-α) cos α - sin (-α) sin α

Solution

Problem 8 :

2 sin θ - cos (90˚ - θ)

Solution

Problem 9 :

sin (-θ) - cos (90˚ - θ)

Solution

Problem 10 :

sin (90˚ - θ) - cos θ

Solution

Problem 11 :

3 cos (-θ) - 4 sin (π/2 - θ)

Solution

Problem 12 :

3 cos θ + sin (π/2 - θ)

Solution

Problem 13 :

cos (π/2 - θ) + 4 sin θ

Solution

Problem 14 :

Explain why sin (θ - ɸ) = -sin (ɸ - θ), cos (θ - ɸ) = cos (ɸ - θ)

Solution

Problem 15 :

Simplify:

sin θ / cos θ

Solution

Problem 16 :

sin (-θ) / cos (-θ)

Solution

Problem 17 :

sin (π/2 - θ) / cos θ

Solution

Problem 18 :

-sin (-θ) / cos θ

Solution

Problem 19 :

cos (π/2 - θ) / sin (π/2 - θ)

Solution

Problem 20 :

cos (π/2 - θ) / cos θ

Solution