Q: Which of the following correctly expresses the sine of an angle $$\theta in a $$right triangle in terms of the lengths of the sides?

$$\sin \theta = \frac{\text{opposite}}{\text{hypotenuse}}$$

Q: Which of the following is the correct reciprocal identity for secant?

$$\sec \theta = \frac{1}{\cos \theta}$$

Q: If $$\sin \theta = \frac{7}{25}$$ and $$\theta is in $$Quadrant II, what is $$\sec \theta$$?

$$\sec \theta = -\frac{25}{24}$$

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

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

Q: A ramp rises 3 feet over a horizontal distance of 4 feet. What is the angle of elevation $$\theta of $$the ramp, to the nearest degree?

$$\theta = \arctan \left( \frac{3}{4} \right ) \approx 37^\circ$$

Q: If $$\cos \theta = -\frac{1}{2}$$ and $$0^\circ \u003c \theta \u003c 360^\circ$$, what are the possible values of $$\theta$$?

$$\theta = 120^\circ or$$ $$240^\circ$$

Q: Which of the following is the correct expression for $$\tan \theta in $$terms of $$\sin \theta$$ and $$\cos \theta$$?

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

Question 1

Which of the following correctly expresses the sine of an angle $$	heta in a $$right triangle in terms of the lengths of the sides?

Accepted Answer

$$\sin 	heta = \frac{	ext{opposite}}{	ext{hypotenuse}}$$

Question 2

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

Accepted Answer

$$\sin 	heta = -\frac{4}{5}$$

Question 3

Which trigonometric function is undefined when $$	heta = 90^\circ$$?

Accepted Answer

$$\cos 	heta$$

Question 4

If $$	an 	heta = \frac{1}{\sqrt{3}}$$, what is the measure of $$	heta in $$degrees in the interval $$0^\circ \u003c 	heta \u003c 90^\circ$$?

Accepted Answer

$$	heta = 30^\circ$$

Question 5

A ladder leans against a wall making a $$60^\circ$$ angle with the ground. If the ladder is 10 ft long, how high up the wall does it reach?

Accepted Answer

$$10 \cdot \sin 60^\circ = 10 \cdot \frac{\sqrt{3}}{2} = 5\sqrt{3} ft$$

Question 6

Which of the following is the correct reciprocal identity for secant?

Accepted Answer

$$\sec 	heta = \frac{1}{\cos 	heta}$$

Question 7

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

Accepted Answer

$$\cos 	heta = -\frac{4}{5}$$

Question 8

Which quadrant is the angle $$210^\circ$$ located in, and which trigonometric functions are positive there?

Accepted Answer

Quadrant III; tangent and cotangent are positive

Question 9

Given $$	an 	heta = \frac{5}{12}$$ and $$	heta is in $$Quadrant I, what is $$\sin 	heta$$?

Accepted Answer

$$\sin 	heta = \frac{5}{13}$$

Question 10

If $$\sin 	heta = \frac{7}{25}$$ and $$	heta is in $$Quadrant II, what is $$\sec 	heta$$?

Accepted Answer

$$\sec 	heta = -\frac{25}{24}$$

Question 11

Which of the following is the correct cofunction identity?

Accepted Answer

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

Question 12

A ramp rises 3 feet over a horizontal distance of 4 feet. What is the angle of elevation $$	heta of $$the ramp, to the nearest degree?

Accepted Answer

$$	heta = \arctan \left( \frac{3}{4} ight ) \approx 37^\circ$$

Question 13

If $$\cos 	heta = -\frac{1}{2}$$ and $$0^\circ \u003c 	heta \u003c 360^\circ$$, what are the possible values of $$	heta$$?

Accepted Answer

$$	heta = 120^\circ or$$ $$240^\circ$$

Question 14

Which of the following is the correct expression for $$	an 	heta in $$terms of $$\sin 	heta$$ and $$\cos 	heta$$?

Accepted Answer

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

Question 15

A Ferris wheel has a radius of 20 meters. What is the height above the ground of a seat at an angle $$	heta = 135^\circ$$ from the horizontal, if the center is 22 meters above the ground?

Accepted Answer

$$22 + 20 \cdot \sin 135^\circ = 22 + 20 \cdot \frac{1}{\sqrt{2}} \approx 36.14$$ meters

Question 16

If $$\sin 	heta = -\frac{1}{2}$$ and $$0^\circ \u003c 	heta \u003c 360^\circ$$, what are the possible values of $$	heta$$?

Accepted Answer

$$	heta = 210^\circ or$$ $$330^\circ$$

Question 17

Which of the following is the correct Pythagorean identity?

Accepted Answer

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

Question 18

If $$\sec 	heta = 8$$ and $$	heta is in $$Quadrant IV, what is $$\sin 	heta$$?

Accepted Answer

$$\sin 	heta = -\frac{\sqrt{63}}{8}$$

Question 19

A surveyor measures the angle of elevation to the top of a building as $$45^\circ$$ from a point 50 meters from the base. How tall is the building?

Accepted Answer

$$50 \cdot 	an 45^\circ = 50$$ meters

Trigonometric Functions and Their Properties: Study Notes for Precalculus

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