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

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

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

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

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 $$\sec \theta$$?

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

Q: A triangle has sides of length 7, 24, and 25. What is $$\tan \theta$$ where $$\theta is $$the angle opposite the side of length 7?

$$\tan \theta = \dfrac{7}{24}$$

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

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