Question

If $\theta$is an acute angle, solve thee equation$\cos \theta =\frac{\sqrt{3}}{2}$.

Short answer

The solution is$\theta =\frac{\mathrm{\pi }}{6}$.

Step-by-step solution

Step 1. Given information

$\theta$ is an acute angle.

Step 2. Calculation

Here $\theta$is an acute angle that is less than $90°$, so the angle is in the first quadrant. Now the equation -

$\cos \theta =\frac{\sqrt{3}}{2}$

$\theta ={\cos }^{-1}\frac{\sqrt{3}}{2}$

$\theta =\frac{\mathrm{\pi }}{6}or30°$