Question

use a calculator to find the value of the acute angle \\( \theta \\) in radians, rounded to three decimal places. \\( \cos \theta = 0.7668 \\) \\( \theta = \square \\) radians (round to three decimal places.)

Explanation:

Step1: Recall the inverse cosine function

To find the angle \(\theta\) when we know \(\cos\theta = 0.7668\), we use the inverse cosine function, \(\theta=\cos^{-1}(0.7668)\).

Step2: Use a calculator in radian mode

Make sure the calculator is set to radian mode. Then, calculate \(\cos^{-1}(0.7668)\). Using a calculator, we find that \(\cos^{-1}(0.7668)\approx0.707\) (after rounding to three decimal places).

Answer:

\(0.707\)