What is cosec^-1 3 in terms of this α =…

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

Question 56

MediumOriginal question

Let $\alpha = \sin^{-1}\left(\frac{1}{3}\right)$ .

What is $\operatorname{cosec}^{-1} 3$ in terms of this $\alpha = \sin^{-1}\left(\frac{1}{3}\right)$ ?

\frac{1}{\alpha}

Correct answerYour answer

\frac{\pi}{2} - \alpha

Correct answerYour answer

\alpha

Correct answerYour answer

\pi - \alpha

Correct answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer C

Correct answer: C

$\operatorname{cosec} \alpha = \frac{1}{\sin \alpha} = 3$ , and $\alpha$ lies in $\left[-\frac{\pi}{2}, \frac{\pi}{2}\right] - \{0\}$ .
So $\operatorname{cosec}^{-1} 3 = \alpha$ .

Worth noting

$\frac{1}{\alpha}$ reads $\operatorname{cosec}^{-1}$ as one over an angle; it is the angle whose cosecant is 3.

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

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