Question

use a half angle identity to find each exact value. cos 195

Answer 1

Hello there! Welcome to OpenStudy!

Quick question about your question, is this in radians or degrees? I am assuming degrees.

Answer 2

cos 195 = cos 390/2
we know cos 390 = cos (360 + 30) = cos 30 = sqrt 3/2

Now we know that

\(2cos^2 \theta = 1 + cos 2 \theta\)
From Half angle Identity
\(2cos^2 \frac{\theta}{2} = 1 + cos \theta\)

Therefore we can write the answer as

\(2cos^2 \frac{390}{2} = 1 + cos ~390\)
OR, \(cos^2 \frac{390}{2} = \frac{2 + \sqrt{3}}{4}\)
OR, \(cos \frac{390}{2} = cos~ 195 ~~= ~\sqrt{\frac{2 + \sqrt{3}}{4}}\)

Understood? :)

Answer 3

thanks i was close but not close enough

Answer 4

:)

Answer 5

:)

Answer 6

WELCOME TO OPENSTUDY !! :)

Answer 7

thank you so much, i'm glad to be here :P

Answer 8

:D AWESOME!