7.4-7.6 Trigonometry Identities

Sec

1/cos

Csc

1/sin

Cot

Cos/sin

Sum and difference formulas

sin (x + y) = sin x cos y + cos x sin y sin (x- y) = sin x cos y - cos x sin y cos (x + y) = cos x cos y - sin x sin y cos (x - y) = cos x cos y + sin x sin y tan (x + y ) = (tan x + tan y)/(1 - tan x tan y) tan (x - y) = (tan x - tan y)/(1 + tan x tan y)

Half angle formulas

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

Double angle formulas

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

Tan

sin/cos

Product to sum formulas

sinx sin y = 1/2 [cos(x - y) - cos(x + y)] cosx cos y = 1/2 [cos(x - y) + cos(x + y)] sinx cos y = 1/2 [sin(x + y) + sin(x - y)] cos x sin y = 1/2 [sin(x + y) - sin(x - y)]

Pythagorean Identities

sin²∅ + cos²∅ = 1 tan²∅ + 1 = sec²∅ cot²∅ + 1 = csc²∅