Level 460 Level 462
Level 461

### Trigonometric Identities

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1/cosθ
secθ reciprocal identity
1/sinθ
cscθ reciprocal identity
1/tanθ
cotθ reciprocal identity
sinθ/cosθ
tanθ quotient identity
cosθ/sinθ
cotθ quotient identity
sin(-θ)
-sinθ odd-even identity
cos(-θ)
cosθ odd-even identity
tan(-θ)
-tanθ odd-even identity
csc(-θ)
-cscθ
sec(-θ)
secθ
cot(-θ)
-cotθ
cos (π/2-θ)
sinθ cofunction identity
sin (π/2-θ)
cosθ cofunction identity
cot (π/2-θ)
tanθ cofunction identity
sec (π/2-θ)
cscθ cofunction identity
csc (π/2-θ)
secθ cofunction identity
tan (π/2-θ)
cotθ cofunction identity
1
sin²θ + cos²θ Pythagorean identity
sec²θ
1 + tan²θ Pythagorean identity
csc²θ
1 + cot²θ Pythagorean identity
sinαcosβ + cosαsinβ
sin(α + β) sum identity
sinαcosβ - cosαsinβ
sin(α - β) difference identity
cosαcosβ - sinαsinβ
cos(α + β) sum identity
cosαcosβ + sinαsinβ
cos(α - β) difference identity
tan(α + β) sum identity
tanα + tanβ/1 - tanαtanβ
tan(α - β) difference identity
tanα - tanβ/1 + tanαtanβ
2 sinθcosθ
sin 2θ double-angle identity
cos²θ - sin²θ
cos 2θ double-angle identity
tan 2θ double-angle identity
2 tanθ/1 - tan²θ
sin½θ half-angle identity
±√1 - cosθ/2
cos½θ half-angle identity
±√1 + cosθ/2
tan½θ half-angle identity
±√1 - cosθ/1 + cosθ
sinαsinβ product-to-sum identity
½[cos(α - β) - cos(α + β)]
cosαcosβ product-to-sum identity
½[cos(α - β) + cos(α + β)]
sinαcosβ product-to-sum identity
½[sin(α + β) - sin(α - β)]
tan(θ) =
sin(θ) ÷ cos(θ)
cot(θ) =
cos(θ) ÷ sin(θ)
sin(θ) =
1 ÷ csc(θ)
cos(θ) =
1 ÷ sec(θ)
tan(θ) =
1 ÷ cot(θ)
csc(θ) =
1 ÷ sin(θ)
sec(θ) =
1 ÷ cos(θ)
cot(θ) =
1 ÷ tan(θ)
-sin(θ)
sin(-θ) =
cos(θ)
cos(-θ) =
-tan(θ)
tan(-θ) =
-csc(θ)
csc(-θ) =
sec(θ)
sec(-θ) =
-cot(θ)
cot(-θ) =
sin(θ)
sin(θ + 2π) =
cos(θ)
cos(θ + 2π) =
tan(θ)
tan(θ + π) =
csc(θ)
csc(θ + 2π) =
cot(θ)
cot(θ + π) =
cos(θ)
sin[(π ÷ 2) − θ] =
sin(θ)
cos[(π ÷ 2) − θ] =
cot(θ)
tan[(π ÷ 2) − θ] =
tan(θ)
cot[(π ÷ 2) − θ] =
1
sin²(θ) + cos²(θ) =
sec²(θ)
1 + tan²(θ) =
csc²(θ)
1 + cot²(θ) =
sin(α)cos(β) + cos(α)sin(β)
sin(α + β) =
cos(α)cos(β) − sin(α)sin(β)
cos(α + β) =
tan(α + β) =
[tan(α) + tan(β)] ÷ [1 − tan(α)tan(β)]
sin(α)cos(β) − cos(α)sin(β)
sin(α − β) =
cos(α)cos(β) + sin(α)sin(β)
cos(α − β) =
tan(α − β) =
[tan(α) − tan(β)] ÷ [1 + tan(α)tan(β)]
2sin(θ)cos(θ)
sin(2θ) =
cos(2θ) =
cos²(θ) − sin²(θ) = 2cos²(θ) − 1 = 1 − 2sin²(θ)
tan(2θ) =
2tan(θ) ÷ [1 − tan²(θ)]
sin(π / 2) =
±√{[1 − cos(θ)] ÷ 2}
cos(π / 2) =
±√{[1 + cos(θ)] ÷ 2}
tan(π / 2) =
±√{[1 − cos(θ)] ÷ [1 + cos(θ)]}
sin²(θ) =
[1 − cos(2θ)] ÷ 2
cos²(θ) =
[1 + cos(2θ)] ÷ 2
tan²(θ) =
[1 − cos(2θ)] ÷ [1 + cos(2θ)]
sin(α) + sin(β) =
2sin[(α + β) ÷ 2]cos[(α − β) ÷ 2]
sin(α) − sin(β) =
2cos[(α + β) ÷ 2]sin[(α − β) ÷ 2]
cos(α) + cos(β) =
2cos[(α + β) ÷ 2]cos[(α − β) ÷ 2]
cos(α) − cos(β) =
-2sin[(α + β) ÷ 2]sin[(α − β) ÷ 2]
sin(α)sin(β) =
[cos(α − β) − cos(α + β)] ÷ 2
cos(α)cos(β) =
[cos(α − β) + cos(α + β)] ÷ 2
sin(α)cos(β) =
[sin(α + β) + sin(α − β)] ÷ 2
cos(α)sin(β) =
[sin(α + β) − sin(α − β)] ÷ 2