Trigonometric Identities + Unit Circle
cos(π)
-1
sin(3π/2)
-1
cot(-θ)
-cotθ
csc(-θ)
-cscθ
sin(-θ)
-sin(θ)
tan(-θ)
-tanθ
sin(0) or sin(π) OR cos(π/2) or cos(3π/2)
0
cos(0)
1
sin(π/2)
1
tan(π/4) or tan(45°)
1
cot²θ + 1 = csc²θ ⇒
1 = csc²θ - cot²θ OR cot²θ = csc²θ - 1
tan²θ + 1 = sec²θ ⇒
1 = sec²θ - tan²θ OR tan²θ = sec²θ - 1
cos(π/3) or cos(60°)
1/2
sin(π/6) or sin(30°)
1/2
secθ
1/cosθ
cscθ
1/sinθ
cotθ
1/tanθ OR cosθ/sinθ
domain and range of tan
D: (-π/2, π/2), R: (-∞,∞)
domain and range of tan^-1
D: (-∞,∞), R: (-π/2, π/2)
domain and range of sin^-1
D: [-1,1], R: [-π/2, π/2]
domain and range of cos^-1
D: [-1,1], R: [0,π]
domain and range of sin
D: [-π/2, π/2], R: [-1,1]
domain and range of cos
D: [0,π] , R: [-1,1]
cos2θ = cos²θ - sin²θ ⇒
cos2θ = 1 - 2sin²θ OR cos2θ = 2cos²θ -1
cos(-θ)
cosθ
sin(π/2 - θ)
cosθ
tan(π/2 - θ)
cotθ
sec(π/2 - θ)
cscθ
csc(π/2 - θ)
secθ
sec(-θ)
secθ
sin2θ
sin2θ = 2sinθcosθ
sin²θ + cos²θ = 1 ⇒
sin²θ - 1 = cos²θ OR cos²θ - 1 = sin²θ
cos(π/2 - θ)
sinθ
tanθ
sinθ/cosθ
tan2θ
tan2θ = 2tanθ/(1-tan²θ)
cot(π/2 - θ)
tanθ
cos(π/4) or cos(45°)
√2/2
sin(π/4) or sin(45°)
√2/2
tan(π/3) or tan(60°)
√3
cos(π/6) or cos(30°)
√3/2
sin(π/3) or sin(60°)
√3/2
tan(π/6) or tan(30°)
√3/3
