sin2 x + cos2 x = 1

Opposites Theorem, for all θ,(flip over x-axis)

Cos (- θ) = cos (θ)Sin (- θ) = - sin (θ)Tan (- θ) = - tan(θ)

For all θ, measured in radians, flip over y

Sin (π - θ) = sin θCos(π - θ) = -cos θTan(π - θ) = -tan θ

Complements TheoremSin (π/2 - θ) = cos θCos(π/2 - θ) = sin θ

For all θ, measured in radians.Cos (π + θ) = -cos θSin(π + θ) = -sin θtan(π + θ) = tan θ

If sin θ = 1/3 , find cos θ

sin2 x + cos2 x = 1 (1/3)2 +cos2x = 1 Cos2x = 8/9

cos( )x or 8

9

2 2

3

2 2

3

If sin x = .681, find sin(-x) and sin (π – x).

Sin (-x) = -sin(x) = -.681

Sin (π – x) = sin x = .681

Using the unit circle, explain why sin (π – θ) = sin θ for all θ

150 30

200 -20

Pages 255 – 2562 – 20

(omit 3, 8, 11, 16)