$$\sin 2\theta = 2 \sin \theta \cos \theta$$

$$\sin \frac{\theta}{2} = \pm \sqrt{\frac{1 - \cos \theta}{2}}$$

Question 1

Which of the following is the correct formula for the Law of Sines used to solve triangles?

Accepted Answer

$$\frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C}$$

Question 2

A population of bacteria doubles every 3 hours. If the initial population is 500, which equation models the population $$P$$ after $$t$$ hours?

Accepted Answer

$$P = 500 \cdot 2$$^{t/3}$$

Question 3

Which of the following is the correct logarithmic form of the exponential equation $$7^x = 50$$?

Accepted Answer

$$x = \log_7$ 50$$

Question 4

Given the polynomial $$f(x) = x^3$ - 4x^2$ + x + 6$$, which value is a zero of the function?

Accepted Answer

$$x = -1$$

Question 5

Which of the following is the correct double angle formula for $$\sin 2	heta$$?

Accepted Answer

$$\sin 2	heta = 2 \sin 	heta \cos 	heta$$

Question 6

If $$\log_2$(x) = 5$$, what is the value of $$x$$?

Accepted Answer

$$x = 32$$

Question 7

Which of the following is the correct expression for the sum of angles identity for cosine?

Accepted Answer

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

Question 8

A right triangle has legs of length 5 and 12. What is the length of the hypotenuse?

Accepted Answer

$$13$$

Question 9

Which of the following is the correct half-angle formula for $$\sin \frac{	heta}{2}$$?

Accepted Answer

$$\sin \frac{	heta}{2} = \pm \sqrt{\frac{1 - \cos 	heta}{2}}$$

Question 10

Solve the system of equations: $$\begin{cases} 2x + 3y = 7 \ x - y = 1 \end{cases}$$

Accepted Answer

$$x = 2, y = 1$$

Question 11

Which of the following is the correct domain for the function $$f(x) = \ln(x-2)$$?

Accepted Answer

$$x \u003e 2$$

Question 12

If $$\sin 	heta = \frac{3}{5}$$ and $$	heta is in $$the first quadrant, what is $$\cos 	heta$$?

Accepted Answer

$$\frac{4}{5}$$

Question 13

Which of the following is the correct binomial expansion for $$(x + 2)^3$?

Accepted Answer

$$x^3$$ + $$6x^2 + 12x + 8$

Question 14

A sound wave has intensity $$I = I_0$ \cdot 10$$^{L/10}$$, where L$ is the decibel level. If L = 20$, what is I$ in terms of I_0$?

Accepted Answer

$$100 I_0$

Question 15

Which of the following is the correct co-function identity?

Accepted Answer

$$\sin(90^\circ - x) = \cos x$$

Question 16

Which of the following is the correct solution to the equation $$2^x = 16$$?

Accepted Answer

$$x = 4$$

Question 17

If $$f(x) = x^2$ - 6x + 8$$, what are the zeros of $$f(x)$$?

Accepted Answer

$$x = 2, x = 4$$

Question 18

Which of the following is the correct formula for the Law of Cosines?

Accepted Answer

$$c^2$$ = $$a^2$$ + $$b^2 - 2ab$$ \cos C$$

College Algebra & Trigonometry for Engineers and Scientists II: Course Syllabus Study Guide

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