Q: A surveyor measures the angle of elevation to the top of a building as $$30^\circ$$ from a point 50 meters from the base. How tall is the building?

$$50 \tan 30^\circ = 50 \cdot \frac{1}{\sqrt{3}} \approx 28.87$$ meters

Q: A wheel of radius 0.5 meters rotates at 120 revolutions per minute. What is the linear speed at the rim in meters per second?

$$2\pi \times 0.5 \times 2 = 2\pi m/s$$

Question 1

A ladder leans against a wall, forming an angle $$	heta$$ with the ground. If the ladder is 10 meters long and the base is 6 meters from the wall, what is the value of $$\sin 	heta$$?

Accepted Answer

$$\frac{8}{10}$$

Question 2

Which of the following is the radian measure for $$60^\circ$$?

Accepted Answer

$$\frac{\pi}{3}$$

Question 3

Given a right triangle with legs of length 1 and $$\sqrt{3}$$, and hypotenuse 2, what is the measure of the smallest angle in radians?

Accepted Answer

$$\frac{\pi}{6}$$

Question 4

If $$	an 	heta = 1$$, and $$0 \u003c 	heta \u003c \pi$$, what is $$	heta$$?

Accepted Answer

$$\frac{\pi}{4}$$

Question 5

A Ferris wheel has a radius of 20 meters. What is the vertical height above the center when a passenger is at an angle of $$30^\circ$$ above the horizontal?

Accepted Answer

$$20 \sin 30^\circ = 10$$ meters

Question 6

Which of the following is the correct value for $$\cos 45^\circ$$?

Accepted Answer

$$\frac{\sqrt{2}}{2}$$

Question 7

If $$\sin 	heta = \frac{1}{2}$$ and $$0 \u003c 	heta \u003c \pi$$, what is $$	heta in $$radians?

Accepted Answer

$$\frac{\pi}{6}$$

Question 8

A ramp rises 3 meters over a horizontal distance of 4 meters. What is the angle of elevation $$	heta of $$the ramp, in radians?

Accepted Answer

$$\arctan \left(\frac{3}{4}\right)$$

Question 9

Which of the following is the period of the function $$y = \sin(2x)$$?

Accepted Answer

$$\pi$$

Question 10

If $$\cos 	heta = 0$$ and $$0 \leq 	heta \u003c 2\pi$$, what are the possible values of $$	heta$$?

Accepted Answer

$$\frac{\pi}{2}$$ and $$\frac{3\pi}{2}$$

Question 11

A point moves around a circle of radius 5 meters at a constant speed, completing one revolution every 10 seconds. What is its angular velocity in radians per second?

Accepted Answer

$$\frac{\pi}{5}$$

Question 12

Which of the following is the correct value for $$	an 60^\circ$$?

Accepted Answer

$$\sqrt{3}$$

Question 13

If $$\sin 	heta = \frac{\sqrt{3}}{2}$$ and $$0 \u003c 	heta \u003c \pi$$, what is $$	heta$$?

Accepted Answer

$$\frac{\pi}{3}$$

Question 14

A surveyor measures the angle of elevation to the top of a building as $$30^\circ$$ from a point 50 meters from the base. How tall is the building?

Accepted Answer

$$50 	an 30^\circ = 50 \cdot \frac{1}{\sqrt{3}} \approx 28.87$$ meters

Question 15

Which of the following is the correct value for $$\sin 90^\circ$$?

Accepted Answer

$$1$$

Question 16

If $$\cos 	heta = -\frac{1}{2}$$ and $$\pi \u003c 	heta \u003c 2\pi$$, what is $$	heta$$?

Accepted Answer

$$\frac{4\pi}{3}$$

Question 17

A wheel of radius 0.5 meters rotates at 120 revolutions per minute. What is the linear speed at the rim in meters per second?

Accepted Answer

$$2\pi 	imes 0.5 	imes 2 = 2\pi m/s$$

Question 18

Which of the following is the correct value for $$\cos 0$$?

Accepted Answer

$$1$$

Question 19

If $$	an 	heta = \sqrt{3}$$ and $$0 \u003c 	heta \u003c \pi$$, what is $$	heta$$?

Accepted Answer

$$\frac{\pi}{3}$$

Fundamental Concepts and Problem Types in Trigonometry

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