## solve 2sin^2(x) + 5cos(x) = 4, sin(2x) = 2cos^2(x)

Trigonometric ratios and functions, the unit circle, inverse trig functions, identities, trig graphs, etc.
spycrab
Posts: 1
Joined: Mon Aug 23, 2010 12:31 am
Contact:

### solve 2sin^2(x) + 5cos(x) = 4, sin(2x) = 2cos^2(x)

Hi guys,
I have 2 equations on my homework that I am not allowed to use a calculator on, and need to find the exact answer/

$2sin^{2}(x)+5cos(x)=4$ where $0 \le x\le360$

And

$sin(2x)=2cos^{2}(x)$ where $0\le x\le 2PI$

stapel_eliz
Posts: 1743
Joined: Mon Dec 08, 2008 4:22 pm
Contact:
spycrab wrote:I have 2 equations on my homework that I am not allowed to use a calculator on....

Why would you try to use a calculator for these? Instead, try using the identities you've learned in trig and the factoring and solving techniques you learned back in algebra:

spycrab wrote:$2sin^{2}(x)+5cos(x)=4$

Apply a Pythagorean identity to convert the sine term to a cosine expression, solve the resulting quadratic-form equation for "cos(x)=", and then solve the two trig equations.

spycrab wrote:$sin(2x)=2cos^{2}(x)$

Convert the sine term using the double-angle formula, move one of the terms across the "equals" sign to join the other term, and factor the result. Then solve the two trig equations.