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Inverse Trigonometric Functions · Question 117 of 120

Question 117

HardOriginal question

What is cos⁡−1(cos⁡(−π3))\cos^{-1}\left(\cos \left(- \frac{\pi}{3}\right)\right)?

Options for question 117

Show the answer and explanation
CorrectNot quiteAnswer B

Correct answer: B

Explanation

  1. cos⁡(−π3)=12\cos \left(- \frac{\pi}{3}\right) = \frac{1}{2}.

  2. The principal value with that cos is π3\frac{\pi}{3}.

Worth noting

−π3-\frac{\pi}{3} is negative, and cos⁡−1\cos^{-1} never returns a negative angle; cos⁡(−π3)=cos⁡π3\cos\left(-\frac{\pi}{3}\right) = \cos \frac{\pi}{3}.

Concept
An inverse function applied to a function
Typical time
120 s
Your time
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The rule this testsValues of expressions
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Ten questions from Inverse Trigonometric Functions, at your own pace.

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Ten questions from Inverse Trigonometric Functions, at your own pace.

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