Pre-Calc: Trig Identites

Pythagorean

cos²theta + sin²theta = 1
tan²theta + 1 = sec²theta
cot²theta + 1 = csc²theta

Co-Function

sintheta = cos(pi/2 - theta)
costheta = sin(pi/2 - theta)
tantheta = cot(pi/2 - theta)
cotrheta = tan(pi/2 - theta)
sectheta = csc(pi/2 - theta)
csctheta = sec(pi/2 - theta)

Even-Odd

sin -theta = -sintheta
csc -theta = -csctheta
cos -theta = costheta
sec -theta = sectheta
tan -theta = -tantheta
cot -theta = -cottheta

Sum of Angles

Sin (A+B) = sinA x cosB + cosA x sinB
Cos(A+B) = cosA x cosB - sinA x sinB
tan (A+B) = tanA + tanB / 1 - tanA x tanB

Difference of Angles

sin (A-B) = sinA x cosB - cosA x sinB
cos (A-B) = cosA x cosB + sinA x sinB
tan (A-B) = tanA - tanB / 1+ tanA x tanB

Double-Angle

sin2theta = 2sintheta x costheta
cos2theta = cos²theta - sin²theta
cos2theta = 1 - 2sin²theta
cos2theta = 2cos²theta - 1
tan2theta = 2tantheta / 1- tan²theta

Half-Angle

sintheta/2 = plus/minus sqrt of 1 - costheta / 2
costheta/2 = plus/minus sqrt of 1 + costheta / 2
tantheta/2 = plus/minus sqrt of 1 - costheta / 1+costheta
tantheta/2 = 1 - costheta / sintheta
tantheta/2 = sintheta / 1 + costheta