Question 1

Find the equation of the tangent line to the curve $y = e^{\sin(x)}$ at $x = \pi$.

Accepted Answer

$y = -e^{-1}(x - \pi)$

Question 2

Evaluate $\arcsin\left(-\frac{\sqrt{3}}{2}\right)$ using the restricted range for $\arcsin$.

Accepted Answer

$-\frac{\pi}{3}$

Question 3

Evaluate $\arccos\left(-\frac{\sqrt{3}}{2}\right)$ using the restricted range for $\arccos$.

Accepted Answer

$\frac{5\pi}{6}$

Question 4

Evaluate $\arctan(-1)$ using the restricted range for $\arctan$.

Accepted Answer

$-\frac{\pi}{4}$

Question 5

Evaluate $\arccos(-2)$ using the restricted range for $\arccos$.

Accepted Answer

Undefined

Question 6

Evaluate $\arcsin\left(\frac{\sqrt{2}}{2}\right)$ using the restricted range for $\arcsin$.

Accepted Answer

$\frac{\pi}{4}$

Question 7

Evaluate $\arctan\left(\frac{1}{\sqrt{3}}\right)$ using the restricted range for $\arctan$.

Accepted Answer

$\frac{\pi}{6}$

Question 8

Evaluate $\arccos(1)$ using the restricted range for $\arccos$.

Accepted Answer

$0$

Question 9

Evaluate $\arccos(0)$ using the restricted range for $\arccos$.

Accepted Answer

$\frac{\pi}{2}$

Question 10

Evaluate $\arccos\left(-\frac{\sqrt{2}}{2}\right)$ using the restricted range for $\arccos$.

Accepted Answer

$\frac{3\pi}{4}$

Question 11

Evaluate $\arctan(0)$ using the restricted range for $\arctan$.

Accepted Answer

$0$

Question 12

Evaluate $\arcsin(-1)$ using the restricted range for $\arcsin$.

Accepted Answer

$-\frac{\pi}{2}$

Question 13

Evaluate $\arccos(0)$ using the restricted range for $\arccos$.

Accepted Answer

$\frac{\pi}{2}$

Question 14

Evaluate $\arccos(-1)$ using the restricted range for $\arccos$.

Accepted Answer

$\pi$

Question 15

Evaluate $\arcsin(-\sqrt{2}/2)$ using the restricted range for $\arcsin$.

Accepted Answer

$-\frac{\pi}{4}$

Question 16

Evaluate $\arccos\left(-\frac{\sqrt{3}}{2}\right)$ using the restricted range for $\arccos$.

Accepted Answer

$\frac{5\pi}{6}$

Question 17

Evaluate $\arcsin\left(\frac{1}{2}\right)$ using the restricted range for $\arcsin$.

Accepted Answer

$\frac{\pi}{6}$

Inverse Trigonometric Functions and Tangent Lines in Calculus

Study Guide - Practice Questions