Question

Find cos2(theta) if cos(theta) =3/4. Do I need to create a triangle, solve for sin, then set it equal to 1-2sin^2(theta)?

Answer 1

Or do I need to us a double angle identity?

Answer 2

either way will work

\[\cos 2\theta = 2 \cos^2 \theta - 1\]

Answer 3

i guess its simpler to just use double angle identity here

Answer 4

hmm...the double and is \[\cos^2\theta-\sin^2\theta\] right?

Answer 5

yes

Answer 6

sorry angle

Answer 7

so since the \[\cos = \frac{ 3 }{ 4 }\] we can replace cos()theta^2 with (3/4)^2?

Answer 8

correct

Answer 9

but what happens to the sin^2(theta)?

Answer 10

\[\sin^2 + \cos^2 = 1\]
make the substitution
\[\sin^2 = 1 - \cos^2\]

Answer 11

that's what I thought

Answer 12

So its going to be\[\frac{ 9 }{ 16 }-(1-\cos^2(\theta) ?\]

Answer 13

Got it! Answer is 1/8.