Question

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

Short answer

The solution is$\theta =45°or\frac{\mathrm{\pi }}{4}$.

Step-by-step solution

Step 1. Given information 

Equation:$\cos \theta =\frac{\sqrt{2}}{2}$

Step 2. Calculation 

Here $\theta$is an acute angle which is less than $90°$, so it is in the first quadrant.

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

$\theta ={\cos }^{-1}\left(\frac{\sqrt{2}}{2}\right)$

$\theta =45°or\frac{\mathrm{\pi }}{4}$