Q: Which of the following is the quotient identity for tangent?

$$\tan x = \frac{\sin x}{\cos x}$$

Question 1

Which of the following functions is one-to-one?

Accepted Answer

$$f(x) = 2x + 3$$

Question 2

Given $$f(x) = 3x - 7$$ and $$g(x) = \frac{x+7}{3}$$, which statement is true?

Accepted Answer

$$f$$ and $$g$$ are inverses because $$f(g(x)) = x$$ and $$g(f(x)) = x$$

Question 3

Evaluate $$e^{\ln 5}.$$

Accepted Answer

$$5$$

Question 4

Which transformation will shift the graph of $$f(x) = e^x$$ two units to the left?

Accepted Answer

$$f(x) = e$$^{x+2}$$

Question 5

Find the domain and vertical asymptote of $$f(x) = \ln(x-4).$$

Accepted Answer

Domain: $$x \u003e 4$$, Vertical asymptote: $$x = 4$$

Question 6

Simplify the expression $$\log_2$ 8 + \log_2$ 4.$$

Accepted Answer

Question 7

A radioactive substance decays according to $$N(t) = N_0$ e$$^{-kt}$$. If the initial amount is 100$ grams and the half-life is 10$ years, what is the value of k$?

Accepted Answer

$$k = \frac{\ln 2}{10}$$

Question 8

Which of the following is the exact value of $$\sin \frac{\pi}{6}$$?

Accepted Answer

$$\frac{1}{2}$$

Question 9

What is the amplitude of $$y = 3 \sin(2x - \frac{\pi}{3})$$?

Accepted Answer

$$3$$

Question 10

Which of the following is a reciprocal trigonometric identity?

Accepted Answer

$$\csc x = \frac{1}{\sin x}$$

Question 11

If $$	heta is a $$reference angle in quadrant III, which of the following is true about $$\sin 	heta$$?

Accepted Answer

$$\sin 	heta is $$negative

Question 12

A surveyor measures the angle of elevation to the top of a building as $$30^\circ$$ from a point $$50$$ meters away. What is the height of the building?

Accepted Answer

$$50 	an 30^\circ$$

Question 13

Which formula expresses the sine of a sum of two angles?

Accepted Answer

$$\sin(A+B) = \sin A \cos B + \cos A \sin B$$

Question 14

Solve for $$x$$: $$2 \sin x = 1$$, where $$0 \leq x \u003c 2\pi.$$

Accepted Answer

$$x = \frac{\pi}{6}, \frac{5\pi}{6}$$

Question 15

Which equation is a Pythagorean identity?

Accepted Answer

$$\sin^2$ x + \cos^2$ x = 1$$

Question 16

A population grows according to $$P(t) = 500 e$$^{0.04t}$$. What is the population after 10$ years?

Accepted Answer

$$500 e$$^{0.4}$$

Question 17

Convert $$270^\circ to $$radians.

Accepted Answer

$$\frac{3\pi}{2}$$

Question 18

Which of the following is the quotient identity for tangent?

Accepted Answer

$$	an x = \frac{\sin x}{\cos x}$$

Question 19

If $$f(x) = \log_{10} x$$, what is $$f(100)$$?

Accepted Answer

$$2$$

Precalculus Study Guide: Functions, Exponentials, Logarithms, and Trigonometry

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