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

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