Chapter 9: Trigonometric Equations and Identities

Question 1

State the negative angle formulae

Answer 1

sin(-θ) = -sinθ
cos(-θ) = cosθ

Question 2

State the supplementary angle formulae

Answer 2

sin(180°- θ) = sinθ OR sin(π- θ) = sinθ

cos(180°- θ) = -cosθ OR cos(π- θ) = -cosθ

Question 3

State the complementary angle formulae

Answer 3

sin(90°- θ) = cos(θ)
cos(90°- θ) = sin(θ)

Question 4

State the pythagorean identity

Answer 4

sin²θ+cos²θ = 1

Question 5

State the double angle identities

Answer 5

sin2θ = 2sinθcosθ

cos2θ
= cos²θ - sin²θ
= 1- 2sin²θ (using pythagorean identity: cos²θ=1-sin²θ)
= 2cos²θ-1(using pythagorean identity: sin²θ=1-cos²θ)