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Inverse Trigonometric Functions · Question 43 of 120

What is sin^-1(-1/3) in terms of this α = sin^-1(1/3)?

Question 43

EasyOriginal question

Let α=sin⁡−1(13)\alpha = \sin^{-1}\left(\frac{1}{3}\right).

What is sin⁡−1(−13)\sin^{-1}\left(-\frac{1}{3}\right) in terms of this α=sin⁡−1(13)\alpha = \sin^{-1}\left(\frac{1}{3}\right)?

Options for question 43

Show the answer and explanation
CorrectNot quiteAnswer A

Correct answer: A

Explanation

  1. sin⁡(−α)=−sin⁡α=−13\sin(-\alpha) = -\sin \alpha = -\frac{1}{3}, and −α-\alpha lies in [−π2,π2]\left[-\frac{\pi}{2}, \frac{\pi}{2}\right].

  2. So sin⁡−1(−13)=−α\sin^{-1}\left(-\frac{1}{3}\right) = -\alpha.

Worth noting

π−α\pi - \alpha is the rule for cos⁡−1\cos^{-1}; for sin⁡−1\sin^{-1} a negative input just flips the sign.

Concept
Principal values of related inputs
Typical time
90 s
Your time
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The rule this testsPrincipal values
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