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Trigonometry

Trigonometric Identities

Double, Half, and power of Angle Identities

tan^2(x) = (1-cos(2x)) / (1+cos(2x))

cos^2(x) = (1+cos (2x)) / 2

sin^2(x) = (1-cos(2x))/2

tan (x/2) = +- √ (1 - cos (x)) / 1+ cos (x)

cos (x/2) = +- √ (1+cos (x))/2

sin (x/2) = +- √ (1-cos(x))/2

tan2x = (2 tan(x)) / 1-tan^2(x)

cos2x = cos^2(x) - sin^2 (x)

sin2x = 2sinxcosx

Sum and Difference Identities

Tan (A+-B) = (Tan A +- Tan B) / (1-+ Tan A TanB)

Cos (A+-B) = CosA CosB -+ SinA SinB

Sin (A+-B) = Sin A CosB +- Sin B Cos A

Pythagorean Identities

1 + cot^2 (x) = csc^2 (x)

tan^2 (x) + 1 = sec^2 (x)

cos^2 (x) = 1 - sin^2 (x)

sin^2 (x) = 1 - cos^2 (x)

sin^2 (x) + cos^2 (x) = 1

Six Trigonometric Functions

Cot A

Adjacent / Opposite

Tan A

Opposite / Adjacent

Sec A

hypotenuse / adjacent

Cos A

Adjacent/ hypotenuse

Csc A

hypotenuse/opposite

Sin A

opposite/ hypotenuse