Posted by **bandit5571** on Tuesday, January 11, 2011 at 11:02pm.

solve the equation

1+4sin(x)=4cos^2(x)

- pre calc -
**bandit5571**, Tuesday, January 11, 2011 at 11:05pm
without a graphing utility

- pre calc -
**Reiny**, Wednesday, January 12, 2011 at 12:08am
1+4sin(x)=4cos^2(x)

1+4sinx = 4(1 - sin^2 x)

4sin^2 x + 4sinx -3 = 0

(2sinx - 1)(2sinx + 3) = 0

sinx = 1/2 or sinx = -3/2

the last part is not possible since sinx is between -1 and +1

so sinx = 1/2

x must be in quadrants I or II

I know sin 30° = 1/2

so x = 30° or 150°

in radians

x = π/6 or x = 5π/6

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