Question

How do you use a half-angle formula to simplify `cos 195`?

Answer 1

Use trig identity `2cos^2a = 1 + cos 2a`

`cos 390 = cos (30 +360) = cos 30 = sqrt3/2`

`2cos^2 195 = 1 + cos 390 = 1 + 0.866 = 1.866`

`cos^2 195 = 1.866/2 = 0.93` -> #

`cos 195 = - 0.97` (Quadrant III)