Q: Which of the following is the correct expression for $$\tan(2x) in $$terms of $$\tan x$$?

$$\dfrac{2 \tan x}{1 - \tan^2$ x}$$

Question 1

Which of the following best describes a function $$f(x)$$?

Accepted Answer

A relation where each input $$x is $$paired with exactly one output $$y.$$

Question 2

Given the function $$f(x) = 2x^2$ - 3x + 1$$, what is $$f(-2)$$?

Accepted Answer

$$15$$

Question 3

Which of the following transformations will reflect the graph of $$y = f(x)$$ over the $$x-$$axis?

Accepted Answer

$$y = -f(x)$$

Question 4

If $$f(x) = x^2$ and g(x) = x + 1$, what is (f$$ \circ g)(2)$$?

Accepted Answer

$$9$$

Question 5

Which of the following is the inverse of $$f(x) = 3x - 5$$?

Accepted Answer

$$f^{-1}(x$$) = \dfrac{x+5}{3}$$

Question 6

A Ferris wheel makes one complete revolution every 60 seconds. If the height $$h (in $$meters) of a seat above the ground at time $$t$$ seconds is modeled by $$h(t) = 10 \sin\left(\dfrac{\pi}{30} t\right) + 15$$, what is the amplitude of the motion?

Accepted Answer

$$10$$

Question 7

Which of the following is equivalent to $$\sin^2$ x + \cos^2$ x$$?

Accepted Answer

$$1$$

Question 8

If $$	an 	heta = 3$$ and $$	heta is in $$the first quadrant, what is $$\sin 	heta$$?

Accepted Answer

$$\dfrac{3}{\sqrt{10}}$$

Question 9

Which of the following is the correct double-angle identity for $$\sin 2x$$?

Accepted Answer

$$2 \sin x \cos x$$

Question 10

A pilot measures the angle of elevation to the top of a mountain as $$25^\circ$$ from a point 2 km from the base. What is the height of the mountain to the nearest tenth of a kilometer?

Accepted Answer

$$0.9 km$$

Question 11

Which of the following is the Law of Sines?

Accepted Answer

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

Question 12

Given $$\cos(\alpha) = -\dfrac{3}{5}$$ and $$\alpha is in $$the third quadrant, what is $$\sin(\alpha)$$?

Accepted Answer

$$-\dfrac{4}{5}$$

Question 13

Which of the following is the correct sum identity for $$\sin(A+B)$$?

Accepted Answer

$$\sin A \cos B + \cos A \sin B$$

Question 14

If $$\sin x = \dfrac{1}{2}$$ and $$x is in$$ $$[0, 2\pi]$$, what are all possible values of $$x$$?

Accepted Answer

$$\dfrac{\pi}{6}, \dfrac{5\pi}{6}$$

Question 15

A triangle has sides $$a = 7$$, $$b = 10$$, and angle $$C = 120^\circ. $$Using the Law of Cosines, what is the length of side $$c$$?

Accepted Answer

$$c = \sqrt{7^2$ + 10^2$ - 2 \cdot 7 \cdot 10 \cos 120^\circ}$$

Question 16

Which of the following is the correct expression for $$	an(2x) in $$terms of $$	an x$$?

Accepted Answer

$$\dfrac{2 	an x}{1 - 	an^2$ x}$$

Question 17

If $$f(x) = x^3$ and g(x$$) = \sqrt{x}$$, what is (f$$ \cdot g)(4)$$?

Accepted Answer

$$32$$

Question 18

A sound wave can be modeled by $$y = 0.5 \cos(440 \pi t)$$, where $$t is in $$seconds. What is the period of the wave?

Accepted Answer

$$\dfrac{1}{220}$$ seconds

Question 19

Which of the following is the correct half-angle identity for $$\sin^2$ x$$?

Accepted Answer

$$\dfrac{1 - \cos 2x}{2}$$

MAT 110: Algebra and Trigonometry - Core Study Guide

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