# Thread: Solving Trig. Equations

1. ## Solving Trig. Equations

A) Determine approximate solutions for this equation in the interval x E [0,2pi] to the nearest hundredth of a radian

cos x - 1/4 = 0

B) Determine an exact solution for this equation in the interval x E [0,2pi]

cos²x - 3/4 = 0

Please help w/steps.

2. Originally Posted by advancedfunctions2010
A) Determine approximate solutions for this equation in the interval x E [0,2pi] to the nearest hundredth of a radian

cos x - 1/4 = 0

B) Determine an exact solution for this equation in the interval x E [0,2pi]

cos²x - 3/4 = 0

Please help w/steps.
$cosx - \frac{1}{4} \implies cosx = \frac{1}{4} \implies x = cos^{-1}\frac{1}{4}$

$cos^{2}x -\frac{3}{4} \implies cos^{2}x = \frac{3}{4} \implies cosx = \pm \frac{\sqrt{3}}{2} \implies x = cos^{-1}\left({\pm \frac{\sqrt{3}}{2}}\right)$

Now find out the corresponding angle x within the given interval