Trigonometry

Purple = on formula sheet

Trig Identities (important)

cos²x + sin²x= 1

tan²x = sec²x - 1

cot²x = cosec²x - 1


Double angle (important)

sin2x = 2sinxcosx

cos2x = cos²x - sin²x

          = 2cos²x - 1   *

          = 1 - 2sin²x   *

*These can be made by rearranging cos²x + sin²x= 1 and subbing it into the equation.


R

R cos (θ ± α) = R cos θ cos α ∓ R sin θ sin α

R sin (θ ± α) = R sin θ cos α ± R cos θ sin α


Instructions

○ Pick the correct formula

○ Compare to equation

○ Put Rcos and Rsin equal to their numbers

○ Square those numbers to find R squared then sqrt

○ Use sin/cos to find tan α

○ Put back into form - shorter equation with one trig identity.


Addition Formulae

sin(A ± B) = sinAcosB ± cosAsinB

cos(A ± B) = cosAcosB ∓ sinAsinB

tan(A ± B) = tanA ± tanB / 1 ∓ tanAtanB


Half angle formulae

Used to find an equation with two of the same trig identities but with different X values

e.g. to find in form sin A + sin B

Given on the formula sheet


Sec


cosec


Cot


Arcsin


Arccos


Arctan