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Chapter 5: Problem 8

Evaluate the expression without using a calculator. \(\arccos 0\)

Short Answer

Expert verified
\(\arccos 0 = \pi/2\)

Step by step solution

01

Recognize the inverse cosine function

The function \(\arccos x\) is the inverse cosine function, meaning it returns the angle whose cosine is \(x\). The range of this function is \([0, \pi]\).
02

Identify the angle

The task is to find an angle \(\theta\) such that \(\cos\theta = 0\). Consider the unit circle, the cosine of an angle essentially corresponds to the x-coordinate of a point on the circle. The x-coordinate is \(0\) at two points: when the angle \(\theta\) is \(\pi/2\) (90 degrees) and when the angle \(\theta\) is \(3\pi/2\) (270 degrees). However, since the range of \(\arccos x\) is \([0, \pi]\), we only consider the angle that falls within this range, which in this case is \(\pi/2\).

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Most popular questions from this chapter

Describe how to find the inverse function of a one-to-one function given by an equation in \(x\) and \(y\). Give an example.

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