Q: Which of the following is the correct definition of $\tan \theta$ in a right triangle?

$\tan \theta = \dfrac{\text{opposite}}{\text{adjacent}}$

Q: Which reciprocal identity is correct?

$\csc \theta = \dfrac{1}{\sin \theta}$

Q: Which of the following is true for complementary angles $\theta$ and $90^\circ - \theta$?

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

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

$\tan \theta = \cot (90^\circ - \theta)$

Q: A ramp rises 3 ft vertically and is 12 ft long. What is the angle $\theta$ the ramp makes with the ground?

$\theta = \arcsin \left( \dfrac{3}{12} \right)$

Q: Which of the following is the correct reciprocal identity for $\sec \theta$?

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

Question 1

Given a right triangle with an angle $	heta$, the side opposite $	heta$ is 5 units and the hypotenuse is 13 units. What is $\sin 	heta$?

Accepted Answer

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

Question 2

Which of the following is the correct definition of $	an 	heta$ in a right triangle?

Accepted Answer

$	an 	heta = \dfrac{	ext{opposite}}{	ext{adjacent}}$

Question 3

If $\sin 	heta = \dfrac{3}{5}$ and $	heta$ is an acute angle, what is $\cos 	heta$?

Accepted Answer

$\cos 	heta = \dfrac{4}{5}$

Question 4

Which reciprocal identity is correct?

Accepted Answer

$\csc 	heta = \dfrac{1}{\sin 	heta}$

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

$10 \cdot \sin 60^\circ$

Question 6

What is the value of $\sin 45^\circ$?

Accepted Answer

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

Question 7

If $	an 	heta = \dfrac{1}{\sqrt{3}}$, what is $	heta$ in degrees?

Accepted Answer

$30^\circ$

Question 8

Which of the following is true for complementary angles $	heta$ and $90^\circ - 	heta$?

Accepted Answer

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

Question 9

A triangle has sides of length 8, 15, and 17. What is the value of $\cos 	heta$ where $	heta$ is the angle opposite the side of length 8?

Accepted Answer

$\cos 	heta = \dfrac{15}{17}$

Question 10

Which of the following is the correct cofunction identity?

Accepted Answer

$	an 	heta = \cot (90^\circ - 	heta)$

Question 11

If $\sin 	heta = 0.6$, what is $	heta$ to the nearest degree?

Accepted Answer

$37^\circ$

Question 12

A ramp rises 3 ft vertically and is 12 ft long. What is the angle $	heta$ the ramp makes with the ground?

Accepted Answer

$	heta = \arcsin \left( \dfrac{3}{12} ight)$

Question 13

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

Accepted Answer

$\sqrt{3}$

Question 14

If $\cos 	heta = 0.8$, what is $\sin 	heta$ for an acute angle $	heta$?

Accepted Answer

$0.6$

Question 15

A surveyor measures the angle of elevation to the top of a building as $40^\circ$ from a point 50 meters away. What is the height of the building?

Accepted Answer

$50 \cdot 	an 40^\circ$

Question 16

Which of the following is the correct reciprocal identity for $\sec 	heta$?

Accepted Answer

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

Question 17

If $\sin 	heta = \dfrac{1}{2}$, what is $	heta$ in degrees?

Accepted Answer

$30^\circ$

Question 18

A triangle has sides of length 7, 24, and 25. What is $	an 	heta$ where $	heta$ is the angle opposite the side of length 7?

Accepted Answer

$	an 	heta = \dfrac{7}{24}$

Question 19

Which of the following is the correct value for $\cos 30^\circ$?

Accepted Answer

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

Trigonometric Functions of Acute Angles: Definitions, Properties, and Applications — 6.1

Study Guide - Practice Questions

Study Guide - Flashcards