pre calc
posted by bandit5571 .
solve the equation
1+4sin(x)=4cos^2(x)

without a graphing utility

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