SOLUTION: I need to solve the equation cos^2(theta) = 4sin(theta)+4, on the interval 0<(theta)<2pi. I thought I had simplified it correctly using trig identities, but something went wrong.

Question 72889: I need to solve the equation cos^2(theta) = 4sin(theta)+4, on the interval 0<(theta)<2pi. I thought I had simplified it correctly using trig identities, but something went wrong. Thanks!
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
use the identity and replace

Now let

Get x to one side

Solve for x

Solutions are and
This means and
Since the first solution doesn't make any sense, ignore it. Solve for

Since is not in the interval 0<(theta)<2pi it can be ignored also
Now find the other value
This allows us to go the other value of sine

There's our other value
So is our answer.

Check:

Our answer works and is in the interval 0<(theta)<2pi

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