Trig Identities

What two angles could you use to find the exact value of sin 105 degrees without a calculator?

60+45

Simplify using the compound angle formula in reverse: cos2xcosx+sin2xsinx

cos(2x-x)

Without your calculator, show: cos75degrees = root6 - root2/ 4

cos(45+30) Use sum and difference formulas

Expand and simplify: sin(90degrees + theta)

costheta

Prove sin2u = 2sinucosu

sin (u+u) = sinucosu +sinucosu = 2sinucosu

Sum and Difference Formulas

sin(u+/- v)= sinucosv +/- cosusinv cos (u+/- v)= cosucosv -/+ sinusinv

Double Angle IDs

sin2u= 2sinucosu cos2u = cos^2u-sin^2u cos2u = 2cos^2u-1 cos2u = 1-2sin^2u

Pythagorean Identities

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