What is the value of tan^-1(1) + cos^-1(-1/2) + sin^-1(-1/2)?

Inverse Trigonometric Functions · Question 90 of 120

Question 90

MediumOriginal question

What is the value of $\tan^{-1}(1) + \cos^{-1}\left(-\frac{1}{2}\right) + \sin^{-1}\left(-\frac{1}{2}\right)$ ?

\frac{\pi}{4}

Correct answerYour answer

\frac{5 \pi}{12}

Correct answerYour answer

\frac{3 \pi}{4}

Correct answerYour answer

\frac{13 \pi}{12}

Correct answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer C

Correct answer: C

Take each principal value on its own branch.
$\frac{\pi}{4} + \frac{2\pi}{3} - \frac{\pi}{6} = \frac{3\pi + 8\pi - 2\pi}{12} = \frac{3\pi}{4}$ .

Worth noting

$\frac{\pi}{4}$ takes $\cos^{-1}\left(-\frac{1}{2}\right)$ as $-\frac{\pi}{3}$ ; on $[0, \pi]$ it is $\frac{2\pi}{3}$ .

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

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