Question 1

What is the derivative of $$\sin x$$ with respect to $$x$$?

Accepted Answer

$$\cos x$$

Question 2

Which of the following correctly expresses the derivative of $$\cos x$$ with respect to $$x$$?

Accepted Answer

$$-\sin x$$

Question 3

If $$y = \cos x$$, what does the graph of $$y' = -\sin x$$ represent?

Accepted Answer

The graph of the slopes of the tangents to $$y = \cos x$$

Question 4

Given $$s = 5 \cos t as $$the position of a weight, what is the velocity $$v as a $$function of $$t$$?

Accepted Answer

$$v = -5 \sin t$$

Question 5

A weight oscillates according to $$s = 5 \cos t. At $$what value of $$t in$$ $$[0, 2\pi]$$ does the velocity reach its maximum positive value?

Accepted Answer

$$t = \pi/2$$

Question 6

If $$y = \cos x$$, what is the slope of the tangent line at $$x = 0$$?

Accepted Answer

0

Question 7

Which of the following statements is true about the relationship between $$y = \cos x$$ and its derivative?

Accepted Answer

The derivative is zero at $$x = 0$$

Question 8

Suppose $$f(x) = \sin x. $$Which of the following best describes the behavior of $$f'(x)$$?

Accepted Answer

$$f'(x) is $$periodic with period $$2\pi$$

Question 9

A pendulum swings such that its position is given by $$s = 5 \cos t. $$What is the acceleration $$a as a $$function of $$t$$?

Accepted Answer

$$a = -5 \cos t$$

Question 10

If $$y = \sin x$$, what is the value of $$y' at$$ $$x = \pi/2$$?

Accepted Answer

0

Question 11

Which of the following best describes the relationship between the graphs of $$y = \cos x$$ and $$y' = -\sin x$$?

Accepted Answer

$$y' = -\sin x is $$the derivative of $$y = \cos x$$

Question 12

If $$f(x) = \sin x$$, what is the second derivative $$f''(x)$$?

Accepted Answer

$$-\cos x$$

Question 13

A weight moves according to $$s = 5 \cos t. At $$what value of $$t in$$ $$[0, 2\pi]$$ does the position reach its minimum?

Accepted Answer

$$t = \pi$$

Question 14

Which of the following is the correct derivative of $$y = a \sin x + b \cos x$$ with respect to $$x$$?

Accepted Answer

$$a \cos x - b \sin x$$

Derivatives of Trigonometric Functions: Calculus Study Notes

Study Guide - Practice Questions