Q: Which of the following is the correct Pythagorean identity?

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

Q: If $$\theta = 270^\circ$$, which trigonometric functions are undefined?

$$\tan \theta$$ and $$\sec \theta$$

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

$$\tan \theta = \dfrac{\sin \theta}{\cos \theta}$$

Question 1

Which of the following best describes a coterminal angle to $$60^\circ$$?

Accepted Answer

$$-300^\circ$$

Question 2

If two angles are complementary, and one angle measures $$x^\circ$$, what is the measure of its complement?

Accepted Answer

$$90^\circ - x^\circ$$

Question 3

Given a right triangle with legs $$a = 5$$ and $$b = 12$$, what is the length of the hypotenuse $$c$$?

Accepted Answer

$$c = 13$$

Question 4

Which of the following is the correct definition of the sine function for an angle $$	heta in $$standard position with terminal side passing through $$(x, y)$$ and distance $$r$$ from the origin?

Accepted Answer

$$\sin 	heta = \dfrac{y}{r}$$

Question 5

A building casts a shadow of $$18 m $$while a flagpole casts a shadow of $$27 m. If $$the building is $$10 m $$high, what is the height of the flagpole?

Accepted Answer

$$15 m$$

Question 6

Which of the following angles is a quadrantal angle?

Accepted Answer

$$90^\circ$$

Question 7

If $$\cos 	heta = -\dfrac{3}{5}$$ and $$	heta is in $$quadrant II, what is $$\sin 	heta$$?

Accepted Answer

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

Question 8

Which of the following is NOT a property of similar triangles?

Accepted Answer

All sides are equal

Question 9

Given $$	an 	heta = \dfrac{y}{x}$$, which of the following is the reciprocal identity for $$\cot 	heta$$?

Accepted Answer

$$\cot 	heta = \dfrac{x}{y}$$

Question 10

If $$\sin 	heta = 0.8$$ and $$	heta is in $$quadrant II, what is $$\cos 	heta$$?

Accepted Answer

$$-0.6$$

Question 11

Which of the following is the correct Pythagorean identity?

Accepted Answer

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

Question 12

If the terminal side of an angle in standard position passes through the point $$(-3, 4)$$, what is $$	an 	heta$$?

Accepted Answer

$$\dfrac{4}{-3}$$

Question 13

Which of the following is the range of the sine function?

Accepted Answer

$$[-1, 1]$$

Question 14

If $$	heta = 270^\circ$$, which trigonometric functions are undefined?

Accepted Answer

$$	an 	heta$$ and $$\sec 	heta$$

Question 15

A disk spins at $$480$$ revolutions per minute. Through how many degrees does a point on the edge move in $$2$$ seconds?

Accepted Answer

$$5760^\circ$$

Question 16

Which of the following is true about vertical angles?

Accepted Answer

They have equal measures

Question 17

If $$	an 	heta = 2$$ and $$	heta is in $$quadrant III, what is the sign of $$\sin 	heta$$?

Accepted Answer

Negative

Question 18

Which of the following is the quotient identity for tangent?

Accepted Answer

$$	an 	heta = \dfrac{\sin 	heta}{\cos 	heta}$$

Question 19

If $$\sin 	heta = -0.5$$ and $$	heta is in $$quadrant IV, what is $$\cos 	heta$$?

Accepted Answer

$$\dfrac{\sqrt{3}}{2}$$

Question 20

Which of the following is NOT a possible value for $$\sec 	heta$$?

Accepted Answer

$$0.5$$

Chapter 1: Trigonometric Functions – Angles, Angle Relationships, and Triangles

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