What is the principal value of tan^-1(-1)?

Inverse Trigonometric Functions · Question 34 of 120

Question 34

EasyOriginal question

What is the principal value of $\tan^{-1}\left(-1\right)$ ?

- \frac{\pi}{2}

Correct answerYour answer

- \frac{\pi}{4}

Correct answerYour answer

\frac{\pi}{4}

Correct answerYour answer

\frac{3 \pi}{4}

Correct answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer B

Correct answer: B

Find the angle $\theta$ in the branch $\left(-\frac{\pi}{2}, \frac{\pi}{2}\right)$ with $\tan \theta = -1$ .
That angle is $- \frac{\pi}{4}$ .

Worth noting

$\tan \frac{3\pi}{4} = -1$ , but $\frac{3\pi}{4}$ is outside $\left(-\frac{\pi}{2}, \frac{\pi}{2}\right)$ .

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

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