Question 1

A 20-foot ladder leans against a wall, making a $$65^\circ$$ angle with the ground. How high up the wall does the ladder reach? (Round your answer to the nearest tenth.)

Accepted Answer

$$18.1$$ feet

Question 2

Which of the following is the correct expression for the Law of Sines?

Accepted Answer

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

Question 3

Given $$\sin 	heta = \dfrac{3}{5}$$ and $$	heta is in $$Quadrant II, what is $$\cos 	heta$$?

Accepted Answer

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

Question 4

A Ferris wheel has a radius of 30 meters. If a passenger is at a position that forms a $$120^\circ$$ central angle from the ground, how high above the ground is the passenger? (Assume the center is 30 meters above the ground.)

Accepted Answer

$$30 + 30 \sin 120^\circ$$

Question 5

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

Accepted Answer

$$2 \sin 	heta \cos 	heta$$

Question 6

Solve for $$x$$: $$2^{x+1} = 16$

Accepted Answer

$$x = 3$$

Question 7

Which of the following is the correct logarithmic form of the equation $$5^x = 125$$?

Accepted Answer

$$x = \log_5$ 125$$

Question 8

A pulley system uses two wheels of radii 8 cm and 12 cm connected by a belt. If the smaller wheel rotates at 15 revolutions per minute, how many revolutions per minute does the larger wheel make?

Accepted Answer

$$10$$ rpm

Question 9

Which of the following is the correct sum-to-product formula for $$\sin A + \sin B$$?

Accepted Answer

$$2 \sin \left( \dfrac{A+B}{2} \right) \cos \left( \dfrac{A-B}{2} \right)$$

Question 10

If $$	an 	heta = 2$$ and $$	heta is in $$Quadrant III, what is $$\sin 	heta$$?

Accepted Answer

$$-\dfrac{2}{\sqrt{5}}$$

Question 11

Which of the following is the correct equation for the ellipse centered at the origin with a major axis of length 10 along the x-axis and a minor axis of length 6 along the y-axis?

Accepted Answer

$$\dfrac{x^2$}{25} + \dfrac{y^2$}{9} = 1$$

Question 12

A triangle has sides $$a = 7$$, $$b = 9$$, and $$c = 12. $$Using the Law of Cosines, what is the measure of angle $$C$$ opposite side $$c$$? (Round to the nearest degree.)

Accepted Answer

$$77^\circ$$

Question 13

Which of the following is the correct expression for the area $$A of a $$triangle with sides $$a$$ and $$b$$ and included angle $$C$$?

Accepted Answer

$$A = \dfrac{1}{2}ab \sin C$$

Question 14

If $$\sin x = 0.6$$ and $$x is in $$Quadrant I, what is $$\cos(2x)$$?

Accepted Answer

$$0.28$$

Question 15

Which of the following is the correct inverse function for $$y = 	an$$^{-1}$$ x$$?

Accepted Answer

$$x = 	an y$$

Question 16

A circle has a central angle of $$2$$ radians and a radius of $$5$$ meters. What is the length of the arc subtended by the angle?

Accepted Answer

$$10$$ meters

Question 17

Which of the following is the correct expression for $$\log_b (MN)$$?

Accepted Answer

$$\log_b M + \log_b N$$

Question 18

If $$\cos 	heta = -0.8$$ and $$	heta is in $$Quadrant III, what is $$\sin 	heta$$?

Accepted Answer

$$-0.6$$

Question 19

Which of the following is the correct polar form of the point $$(3, 3\sqrt{3})$$?

Accepted Answer

$$(6, \dfrac{\pi}{3})$$

Precalculus Trigonometry: Course Structure, Topics, and Key Concepts (MATH 110 Syllabus Study Guide)

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