Trigonometric Identities

cos(a/2)

+- (1+cos(a)/2)^(1/2)

tan (a/2)

+- (1-cos(a)/1+cos(a))^(1/2)

sin(a/2)

+-(1-cos(a)/2)^1/2

cot(-x)

-cotx

csc(-x)

-cscx

sin(-x)

-sinx

tan(-x)

-tanx

sin^2x + cos^2x

1

cos(2x)

1) cos^2x-sin^2x 2) 1-2sin^2x 3) 2cos^2x-1

cotx

1) cosx/sinx 2) 1/tanx

Reciprocal Identities

1) cscx = 1/sinx 2) secx = 1/cosx 3) cotx = 1/tanx

Double Angle Formulas

1) sin(2x) = 2sinxcosx 2) cos(2x) = cos^2x-sin^2x 3) cos(2x) = 1-2sin^2x 4) cos (2x) = 2cos^2x-1 5) tan (2x) = 2tanx/1-tan^2x 6) sin^2x = 1-cos(2x)/2 7) cos^2x = 1+ cos(2x)/2 8) tan^2x = 1-cos(2x)/1+cos(2x)

Half Angle Formulas

1) sin^2(a/2) = 1-cos(a)/2 2) cos^2(a/2) = 1+cos(a)/2 3) cos^2(a/2) = 1+cos(a)/2 4) tan^2(a/2) = 1-cos(a)/1+cos(a) 5) sin(a/2) = +-(1-cos(a)/2)^1/2 6) cos(a/2) = +- (1+cos(a)/2)^(1/2) 7) tan (a/2) = +- (1-cos(a)/1+cos(a))^(1/2) 8) tan (a/2) = +- (1-cos(a)/sin(a))

Quotient Identities

1) tanx = sinx/cosx 2) cotx = cosx/sinx

secx

1/cosx

cscx

1/sinx

sin(2x)

2sinxcosx

tan(2x)

2tanx/1-tan^2x

cos(-x)

cosx

tan^2x + 1

csc^2x

cot^2x+1

cscx

sec(-x)

secx

Pythagorean Identities

sin^2x +cos^2 = 1 tan^2x +1 = sec^2x cot^2x +1 = csc^2x

tanx

sinx/cosx