Q: Convert $$6.25\pi$$ radians to degrees. What is the correct value?

$$6.25\pi \times \frac{180}{\pi} = 1125^\circ$$

Q: A building is 125 ft away from a point on the ground. If the angle of elevation to the top of the building is $$62.5^\circ$$, how tall is the building?

$$125 \tan 62.5^\circ = 240\ \text{ft}$$

Q: If $$\tan \theta = -5.12$$, find all possible values of $$\theta in$$ $$0^\circ \u003c \theta \u003c 360^\circ.$$

$$\theta = 101.3^\circ$$ and $$281.3^\circ$$

Q: If $$\cos \theta = 0.810$$, find all possible values of $$\theta in$$ $$0^\circ \u003c \theta \u003c 360^\circ.$$

$$\theta = 36^\circ$$ and $$324^\circ$$

Q: If $$\sec \theta = -1.80$$, find all possible values of $$\theta in$$ $$0^\circ \u003c \theta \u003c 360^\circ.$$

$$\theta = 123^\circ$$ and $$236^\circ$$

Q: Convert $$0.5$$ revolutions to degrees.

$$0.5 \times 360^\circ = 180^\circ$$

Question 1

Convert $$6.25\pi$$ radians to degrees. What is the correct value?

Accepted Answer

$$6.25\pi 	imes \frac{180}{\pi} = 1125^\circ$$

Question 2

If $$\sin 	heta = \frac{2}{3}$$ and $$	heta is in $$Quadrant II, what is $$\cos 	heta$$?

Accepted Answer

$$-\frac{\sqrt{5}}{3}$$

Question 3

Given $$	an 	heta = \frac{3}{\sqrt{5}}$$ and $$	heta is in $$Quadrant III, what is $$\sin 	heta$$?

Accepted Answer

$$-\frac{3}{\sqrt{14}}$$

Question 4

Express $$\sec 211.5^\circ in $$terms of a primary trigonometric function and evaluate it using a calculator in DEG mode.

Accepted Answer

$$\sec 211.5^\circ = -1.91$$

Question 5

A building is 125 ft away from a point on the ground. If the angle of elevation to the top of the building is $$62.5^\circ$$, how tall is the building?

Accepted Answer

$$125 	an 62.5^\circ = 240\ 	ext{ft}$$

Question 6

Solve the right triangle where $$A = 36.5^\circ$$ and $$c = 7.18. $$What is the length of side $$a$$?

Accepted Answer

$$a = 7.18 \sin 36.5^\circ \approx 4.27$$

Question 7

If $$	an 	heta = -5.12$$, find all possible values of $$	heta in$$ $$0^\circ \u003c 	heta \u003c 360^\circ.$$

Accepted Answer

$$	heta = 101.3^\circ$$ and $$281.3^\circ$$

Question 8

Express $$\csc 2.65 in $$terms of a primary trigonometric function and evaluate it using a calculator in RAD mode.

Accepted Answer

$$\csc 2.65 = \frac{1}{\sin 2.65} \approx 2.75$$

Question 9

Given $$\sec 5.875$$ radians, express it in terms of a primary trigonometric function and evaluate.

Accepted Answer

$$\sec 5.875 = \frac{1}{\cos 5.875} \approx 1.09$$

Question 10

If $$\cos 	heta = 0.810$$, find all possible values of $$	heta in$$ $$0^\circ \u003c 	heta \u003c 360^\circ.$$

Accepted Answer

$$	heta = 36^\circ$$ and $$324^\circ$$

Question 11

Solve the right triangle where $$B = 21.5^\circ$$ and $$a = 4.27. $$What is the length of side $$c$$?

Accepted Answer

$$c = \frac{4.27}{\sin 21.5^\circ} \approx 11.68$$

Question 12

If $$\sec 	heta = -1.80$$, find all possible values of $$	heta in$$ $$0^\circ \u003c 	heta \u003c 360^\circ.$$

Accepted Answer

$$	heta = 123^\circ$$ and $$236^\circ$$

Question 13

Convert $$0.5$$ revolutions to degrees.

Accepted Answer

$$0.5 	imes 360^\circ = 180^\circ$$

Question 14

If $$\sin 	heta = 0.5$$ and $$	heta is in $$Quadrant II, what is $$	heta in $$degrees?

Accepted Answer

$$	heta = 150^\circ$$

Question 15

Given $$	an 	heta = 2.71$$ and $$c = 3.66 in a $$right triangle, what is the length of side $$a$$?

Accepted Answer

$$a = c \sin A = 3.66 \sin 70.4^\circ \approx 3.44$$

Precalculus Study Notes: Trigonometric Functions, Angles, and Right Triangle Applications

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