Trigonometric Identities Table

The trigonometric identities are used for solving trigonometric equations. The trigonometric identities are based on the trigonometric functions of one or more angles. The pythagorean trig identities chart given here expresses the six trigonometric functions in terms of other five functions.That is the trigonometric identities table helps to express any trigonometric function in terms of any other.


Pythagorean Trig Identities

  Sin(θ) Cos(θ) Tan(θ) Csc(θ) Sec(θ) Cot(θ)
Sin(θ) = sin(θ) ± √1 - cos²(θ)
± tan(θ)
√1 + tan²(θ)
1
csc(θ)
±
√sec²(θ) - 1
sec(θ)
± 1
√1 + cot²(θ)
Cos(θ) = ± √1 - sin²(θ) cos(θ)
± 1
√1 + tan²(θ)
±
√csc²(θ) - 1
csc(θ)
1
sec(θ)
± cot(θ)
√1 + cot²(θ)
Tan(θ) =
± sin(θ)
√1 - sin²(θ)
±
√1 - cos²(θ)
cos(θ)
tan(θ)
± 1
√csc²(θ) - 1
± √sec²(θ) - 1
1
cot(θ)
Csc(θ) =
1
sin(θ)
± 1
√1 - cos²(θ)
±
√1 + tan²(θ)
tan(θ)
csc(θ)
± sec(θ)
√sec²(θ) - 1
± √1 + cot²(θ)
Sec(θ) =
± 1
√1 - sin²(θ)
1
cos(θ)
± √1 + tan²(θ)
± csc(θ)
√csc²(θ) - 1
sec(θ)
±
√1 + cot²(θ)
cot(θ)
Cot(θ) =
±
√1 - sin²(θ)
sin(θ)
± cos(θ)
√1 - cos²(θ)
1
tan(θ)
± √csc²(θ) - 1
± 1
√sec²(θ) - 1
cot(θ)

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