Question
Find the exact value of the following expression. \( \cos ^{-1}(-1) \) Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. \( \cos ^{-1}(-1)=\square \) (Simplify your answer. Type an exact answer, using \( \pi \) as needed. Use integers or fractions for any numbers in the expression.) B. The function is not defined.
Ask by Hodges Tucker. in the United States
Dec 03,2024
Upstudy AI Solution
Tutor-Verified Answer
Answer
\( \cos^{-1}(-1)=\pi \)
Solution
Calculate or simplify the expression \( \arccos(-1) \).
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 \( \pi \).
Therefore, the correct choice is:
A. \( \cos^{-1}(-1)=\pi \)
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Simplify this solution Bonus Knowledge
A. \( \cos ^{-1}(-1)=\pi \) The inverse cosine function, \( \cos^{-1}(x) \), gives the angle whose cosine is \( x \). Since \( \cos(\pi) = -1 \), the exact value is \( \pi \).
