Question 1

Given the right triangle shown, if $$a = 8$$ and $$b = 15$$, what is the length of $$c$$?

Accepted Answer

$$c = 17$$

Question 2

In the right triangle above, if $$\angle A = 30^\circ$$ and $$c = 10$$, what is the value of $$a$$?

Accepted Answer

$$a = 5$$

Question 3

If $$	riangle ABC is a $$right triangle with $$\angle C = 90^\circ$$, which trigonometric function represents $$\frac{a}{c}$$?

Accepted Answer

$$\sin A$$

Question 4

Given the bearing diagram, what is the bearing from $$O to$$ $$B if $$the angle from North to $$OB is$$ $$41^\circ$$ west of North?

Accepted Answer

$$N\ 41^\circ\ W$$

Question 5

A ship leaves port and travels on a bearing of $$N\ 33^\circ\ W$$ for 24 miles, then turns $$90^\circ$$ and travels $$S\ 57^\circ\ W$$ for 5 miles. What is the bearing of the ship from port?

Accepted Answer

$$N\ 44.8^\circ\ W$$

Question 6

If $$\sin$$^{-1}$$\left(\frac{4}{5}ight) is$$ $$	heta$$, what is $$\cos 	heta$$?

Accepted Answer

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

Question 7

A building 300 feet tall casts a 60 foot long shadow. What is the angle of elevation of the sun to the nearest degree?

Accepted Answer

$$11^\circ$$

Question 8

A radio tower is 170 feet tall. How long should a guy wire be if it is attached 10 feet from the top and makes a $$30^\circ$$ angle with the ground?

Accepted Answer

$$320.0$$ feet

Question 9

If $$	an$$^{-1}$$(x) is$$ $$	heta$$, what is $$\sin 	heta in $$terms of $$x$$?

Accepted Answer

$$\frac{x}{\sqrt{x^2$+1}}$$

Question 10

A boat travels 16 miles on a bearing of $$N\ 38^\circ\ E. $$How many miles north and east has the boat traveled?

Accepted Answer

12.6 miles north and 9.9 miles east

Question 11

Given $$d = -4 \sin 3t$$ meters, what is the period of the motion?

Accepted Answer

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

Question 12

If $$\cos$$^{-1}$$\left(\frac{1}{4}ight) is$$ $$	heta$$, what is $$	heta in $$radians rounded to two decimal places?

Accepted Answer

$$1.32$$

Question 13

If $$\sin$$^{-1}$$(0.8) is$$ $$	heta$$, what is $$	heta in $$radians rounded to two decimal places?

Accepted Answer

$$0.93$$

Question 14

If $$	an$$^{-1}$$(0.2) is$$ $$	heta$$, what is $$	heta in $$radians rounded to two decimal places?

Accepted Answer

$$0.20$$

Question 15

If $$\cos(\sin$$^{-1}$$ x)$$, where $$x is in$$ $$[0,1]$$, what is the expression in terms of $$x$$?

Accepted Answer

$$\sqrt{1-x^2$}$$

Question 16

If $$	an(\sec$$^{-1}$$ \frac{x^2$+4}{x})$$, what is the expression in terms of $$x$$?

Accepted Answer

$$\frac{2}{x}$$

Question 17

A straight trail with a uniform inclination of $$17^\circ$$ leads from a lodge at an elevation of 800 feet to a mountain lake at an elevation of 9,800 feet. What is the length of the trail to the nearest foot?

Accepted Answer

$$30,783$$ feet

Question 18

If $$\sin(	an$$^{-1}$$ x)$$, what is the expression in terms of $$x$$?

Accepted Answer

$$\frac{x}{\sqrt{x^2$+1}}$$

Question 19

If $$\cos(	an$$^{-1}$$ x)$$, what is the expression in terms of $$x$$?

Accepted Answer

$$\frac{1}{\sqrt{x^2$+1}}$$

Step-by-Step Guidance for Trigonometry Test 2 Review (Sections 5.5-5.8)

Study Guide - Practice Questions

Study Guide - Flashcards