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

$$\frac{\text{opposite}}{\text{adjacent}}$$

Q: Which of the following is a cofunction identity?

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

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

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

Question 1

Given a right triangle where one acute angle $$	heta$$ has an opposite side of length 5, an adjacent side of length 12, and a hypotenuse of length 13, what is $$\sin 	heta$$?

Accepted Answer

$$\frac{12}{13}$$

Question 2

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

Accepted Answer

$$\frac{	ext{opposite}}{	ext{adjacent}}$$

Question 3

If $$\sin \beta = \frac{6}{7}$$ for an acute angle $$\beta$$, what is $$\cos \beta$$?

Accepted Answer

$$\frac{\sqrt{13}}{7}$$

Question 4

A ladder is placed so that it reaches 25 ft up a wall and its base is 6.5 ft from the wall. What is the angle $$	heta$$ the ladder makes with the ground? (Round to the nearest degree.)

Accepted Answer

$$75^\circ$$

Question 5

Which of the following is a true statement about similar right triangles and trigonometric ratios?

Accepted Answer

The trigonometric ratios depend only on the measure of the angle.

Question 6

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

Accepted Answer

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

Question 7

A firework is launched at a $$60^\circ$$ angle and travels 390 ft horizontally. What is the approximate height of the firework at its peak? (Round to the nearest foot.)

Accepted Answer

675 ft

Question 8

If $$\sin 	heta = 0.5$$ for an acute angle $$	heta$$, what is $$	heta in $$degrees?

Accepted Answer

$$30^\circ$$

Question 9

Which of the following is a cofunction identity?

Accepted Answer

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

Question 10

Given $$	an \alpha = \frac{5}{12}$$ for an acute angle $$\alpha$$, what is $$\sin \alpha$$?

Accepted Answer

$$\frac{5}{13}$$

Question 11

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

Accepted Answer

$$0.6$$

Question 12

Which trigonometric function is the reciprocal of $$\sec 	heta$$?

Accepted Answer

$$\cos 	heta$$

Question 13

If $$\sin 30^\circ = \frac{1}{2}$$, what is $$\cos 60^\circ$$?

Accepted Answer

$$\frac{1}{2}$$

Question 14

A right triangle has legs of length 1 and hypotenuse $$\sqrt{2}. $$What is the measure of each acute angle?

Accepted Answer

$$45^\circ$$

Question 15

If $$\sin 	heta = 0.6$$ and $$	heta is $$acute, what is $$	an 	heta$$?

Accepted Answer

$$0.75$$

Question 16

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

Accepted Answer

$$\sqrt{3}$$

Question 17

If $$\sin 	heta = 0.5$$, what is $$\cos (90^\circ - 	heta)$$?

Accepted Answer

$$0.5$$

Question 18

A right triangle has an angle $$	heta$$ such that $$\cos 	heta = 0.4. $$What is $$	heta to $$the nearest degree?

Accepted Answer

$$66^\circ$$

Question 19

If $$\sin 	heta = \frac{3}{5}$$ for an acute angle $$	heta$$, what is $$\csc 	heta$$?

Accepted Answer

$$\frac{5}{3}$$

Question 20

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

Accepted Answer

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

Trigonometric Functions of Acute Angles: Right Triangle Approach

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