Evaluate the expression. cos − 1 ( 0 ) \cos^{-1}\left(0\right) cos − 1 ( 0 )

In this problem, we're asked to evaluate the expression the inverse cosine of 0. Now, when working with inverse trig functions we know that we can also think of this as okay, the cosine of what angle is equal to 0, and we want to find the angle for which that is true. Now I don't really need to worry about the sine of my values here being positive or negative because we're working with the number 0, so I actually know that it has to be right in between those on my y axis. So within my interval from 0 to pi that we must stay within when working with the inverse cosine, I know that the cosine of pi over 2 is going to be equal to 0. So that represents my solution

5. Inverse Trigonometric Functions and Basic Trigonometric Equations

Inverse Sine, Cosine, & Tangent

Trigonometry

5. Inverse Trigonometric Functions and Basic Trigonometric Equations

Inverse Sine, Cosine, & Tangent

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Multiple Choice

Evaluate the expression.
$\cos^{-1}\left(0\right)$

$0$

$\frac{\pi}{2}$

$\pi$

$\frac{3\pi}{2}$

Verified step by step guidance

Understand the problem: We need to evaluate the expression $ \cos^{-1}(0) $. This involves finding the angle whose cosine is 0.

Recall the range of the $ \cos^{-1} $ function: The inverse cosine function, $ \cos^{-1}(x) $, returns values in the range $[0, \pi]$.

Identify the angle: The cosine of an angle is 0 at $ \frac{\pi}{2} $ and $ \frac{3\pi}{2} $. However, since $ \cos^{-1}(x) $ only returns values between $ 0 $ and $ \pi $, we focus on $ \frac{\pi}{2} $.

Verify the solution: Check that $ \cos(\frac{\pi}{2}) = 0 $ to ensure that $ \frac{\pi}{2} $ is indeed the correct angle.

Conclude the evaluation: The value of $ \cos^{-1}(0) $ is $ \frac{\pi}{2} $.