Question

sin4theta = cos2theta
please solve for -pi ≤ theta ≤ pi

Answer 1

is it

\[\sin(4\theta) = \cos(2 \theta)\]

or

\[\sin^4(\theta) = \cos^2{\theta}\]

Answer 2

the first one: sin(4θ)=cos(2θ)

Answer 3

ok use the double angle expansion

\[\sin(2(2\theta)) = 2\sin(2\theta)\cos(2\theta)\]

than then you have

\[2\sin(2\theta)\cos(2\theta) = \cos(2\theta)\]

this should make it easier...

Answer 4

divide both sides by

\[\cos(2 \theta)\]

Answer 5

\[\sin 4\theta = \sin(2\theta+2\theta) = 2\sin(2\theta)\cos(2\theta)\ = \cos(2\theta)\] cancel the \[\cos2\theta\] from both sides and you got \[\sin2\theta = \frac{ 1 }{ 2 } 2\theta = 30 and \theta = 15°\]

Answer 6

thx so much for all your help :D

Answer 7

the only problem is that's not the complete solution, you need to check the defined domain.

Answer 8

?? defined domain?
btw doesn't dividing both sides by cos2θ make you lose some roots?

Answer 9

@alexnhchong You are losing the possible root of θ when cos(2θ) = 0

Answer 10

So you can always just check that if you're concerned.

Answer 11

ic. again, thx a lot to those who helped :)