In which interval does this θ = cos^-1(-3/5)…

In which interval does this θ = cos^-1(-3/5) lie?

Question 85

EasyOriginal question

Let $\theta = \cos^{-1}\left(-\frac{3}{5}\right)$ .

In which interval does this $\theta = \cos^{-1}\left(-\frac{3}{5}\right)$ lie?

\left(0, \frac{\pi}{2}\right)

Correct answerYour answer

\left(-\frac{\pi}{2}, 0\right)

Correct answerYour answer

\left(\pi, \frac{3\pi}{2}\right)

Correct answerYour answer

\left(\frac{\pi}{2}, \pi\right)

Correct answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer D

Correct answer: D

$\cos^{-1}$ takes values in $[0, \pi]$ .
A negative cosine on $[0, \pi]$ means an obtuse angle: $\left(\frac{\pi}{2}, \pi\right)$ .

Worth noting

$\left(-\frac{\pi}{2}, 0\right)$ is where $\sin^{-1}$ of a negative number lies, not $\cos^{-1}$ .

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

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