Question
Participation Activity \#7 This is similar to Try It \#2c in the OpenStax text. Evaluate \( \cos ^{-1}(-1) \) Enter the exact answer.
Ask by Garrett Peters. in the United States
Feb 18,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
\( \cos^{-1}(-1) = \pi \)
Solution
Calculate or simplify the expression \( \cos^{-1}(-1) \).
Calculate the value by following steps:
- step0: Calculate:
\(\arccos\left(-1\right)\)
- step1: Calculate the trigonometric value:
\(\pi \)
The exact value of \( \cos^{-1}(-1) \) is \( \pi \).
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Simplify this solution Extra Insights
The angle whose cosine is -1 is \( \pi \) radians (or 180 degrees). This is because the cosine function reaches -1 at \( \pi \), which is located on the negative x-axis of the unit circle. Therefore, \( \cos^{-1}(-1) = \pi \). To illustrate the concept visually, think about the unit circle: as you traverse the circle counterclockwise starting from (1,0), you reach the point (-1,0) at exactly \( \pi \) radians. So, there you have it, the inverse cosine of -1 lands you right on the opposite side of the circle!
