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Chapter 5: Problem 7

Evaluate the expression without using a calculator. \(\arccos \frac{1}{2}\)

Short Answer

Expert verified
\(\arccos \frac{1}{2}= \frac{\pi}{3}\) radians.

Step by step solution

01

- Evaluate the arccosine function

The \(\arccos\) function gives us the angle whose cosine is the number we input. Therefore, we need to recall the unit circle and trigonometric values of certain angles to find an angle whose cosine is \(\frac{1}{2}\).
02

- Identify the corresponding angle

On recalling the unit circle, we know that the cosine of 60 degrees or \(\frac{\pi}{3}\) radians in the first quadrant equals \(\frac{1}{2}\). Therefore, \(\arccos\frac{1}{2}=\frac{\pi}{3}\) radians.

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