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
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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
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Joined: Mon Dec 08, 2008 4:22 pm
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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:
$2sin^{2}(x)+5cos(x)=4$
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.
$sin(2x)=2cos^{2}(x)$
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.