Q: 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? (Use $$\sin 60^\circ.)$$

$$10 \times \dfrac{\sqrt{3}}{2} = 5\sqrt{3} ft$$

Q: Which reciprocal identity is correct?

$$\cot \theta = \dfrac{1}{\tan \theta}$$

Q: A ramp rises at an angle of $$30^\circ to $$the horizontal. If the ramp is 8 meters long, what is the vertical height? (Use $$\sin 30^\circ.)$$

$$8 \times \dfrac{1}{2} = 4 m$$

Q: A surveyor measures the angle of elevation to the top of a building as $$60^\circ. If $$she is standing 20 meters from the base, how tall is the building? (Use $$\tan 60^\circ.)$$

$$20 \times \sqrt{3} = 20\sqrt{3} m$$

Q: A circle has a radius of 5 meters. What is the length of the arc subtended by a central angle of $$\dfrac{\pi}{3}$$ radians?

$$5 \times \dfrac{\pi}{3} = \dfrac{5\pi}{3} m$$

Q: If $$\theta = 3\pi/2$$ radians, what are the values of $$\sin \theta$$ and $$\cos \theta$$?

$$\sin \theta = -1,\ \cos \theta = 0$$

Question 1

Which of the following correctly gives the value of $$\sin 45^\circ$$ and $$\cos 45^\circ$$?

Accepted Answer

$$\sin 45^\circ = \dfrac{\sqrt{2}}{2},\ \cos 45^\circ = \dfrac{\sqrt{2}}{2}$$

Question 2

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? (Use $$\sin 60^\circ.)$$

Accepted Answer

$$10 	imes \dfrac{\sqrt{3}}{2} = 5\sqrt{3} ft$$

Question 3

Which of the following angles has a tangent value that is undefined?

Accepted Answer

$$90^\circ$$

Question 4

If $$\cos 	heta = -\dfrac{1}{2}$$ and $$	heta is $$between $$90^\circ$$ and $$180^\circ$$, what is $$\sin 	heta$$?

Accepted Answer

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

Question 5

Which reciprocal identity is correct?

Accepted Answer

$$\cot 	heta = \dfrac{1}{	an 	heta}$$

Question 6

A Ferris wheel makes one complete revolution. What is the radian measure of the angle swept out?

Accepted Answer

$$2\pi$$ radians

Question 7

If $$\sin 	heta = 0$$, which of the following could be a possible value for $$	heta in $$degrees?

Accepted Answer

$$180^\circ$$

Question 8

A ramp rises at an angle of $$30^\circ to $$the horizontal. If the ramp is 8 meters long, what is the vertical height? (Use $$\sin 30^\circ.)$$

Accepted Answer

$$8 	imes \dfrac{1}{2} = 4 m$$

Question 9

Which of the following is the correct value for $$	an 150^\circ$$?

Accepted Answer

$$-\dfrac{\sqrt{3}}{3}$$

Question 10

If $$\sin 	heta = 1$$, what is the value of $$	heta in $$radians between $$0$$ and $$2\pi$$?

Accepted Answer

$$\dfrac{\pi}{2}$$

Question 11

A rotating platform turns through $$135^\circ. $$What is this angle in radians?

Accepted Answer

$$\dfrac{3\pi}{4}$$

Question 12

Which of the following is the correct value for $$\cos 120^\circ$$?

Accepted Answer

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

Question 13

If $$	an 	heta = 1$$, which of the following could be $$	heta$$ between $$0^\circ$$ and $$360^\circ$$?

Accepted Answer

$$45^\circ$$

Question 14

A surveyor measures the angle of elevation to the top of a building as $$60^\circ. If $$she is standing 20 meters from the base, how tall is the building? (Use $$	an 60^\circ.)$$

Accepted Answer

$$20 	imes \sqrt{3} = 20\sqrt{3} m$$

Question 15

Which of the following is the correct value for $$\sin 270^\circ$$?

Accepted Answer

$$-1$$

Question 16

If $$\cos 	heta = 0$$, which of the following is a possible value for $$	heta$$ between $$0^\circ$$ and $$360^\circ$$?

Accepted Answer

$$90^\circ$$

Question 17

Which of the following is the correct value for $$\sin 150^\circ$$?

Accepted Answer

$$\dfrac{1}{2}$$

Question 18

A circle has a radius of 5 meters. What is the length of the arc subtended by a central angle of $$\dfrac{\pi}{3}$$ radians?

Accepted Answer

$$5 	imes \dfrac{\pi}{3} = \dfrac{5\pi}{3} m$$

Question 19

Which of the following is the correct value for $$	an 120^\circ$$?

Accepted Answer

$$-\sqrt{3}$$

Question 20

If $$	heta = 3\pi/2$$ radians, what are the values of $$\sin 	heta$$ and $$\cos 	heta$$?

Accepted Answer

$$\sin 	heta = -1,\ \cos 	heta = 0$$

Essential Trigonometric Values and Identities

Study Guide - Practice Questions

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