basic identities involving sines , cosines, and tangents
Post on 04-Jan-2016
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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)
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