Trigonometric Functions Practice Test

Review the following concepts if needed:

• The Right Triangle Model Help
• Pythagorean Extras Help
• Trigonometric Identities Help

Trigonometric Functions Practice Test

A good score is eight correct.

1. Refer to Fig. 2-6. The tangent of ∠ABC is equal to

(a) the length of line segment AC divided by the length of line segment AB

(b) the length of line segment AD divided by the length of line segment BD

(c) the length of line segment AD divided by the length of line segment AB

(d) no ratio of lengths that can be shown here

Fig. 2-6 . Illustration for quiz questions.

2. Refer to Fig. 2-6. Suppose we know that the measure of ∠BCA is 50° and the length of line segment AD is 5.3 units. What is the length of line segment AC? Express your answer to one decimal place (that is, the nearest tenth of a unit). Use a calculator if necessary.

(a) 6.9 units

(b) 8.2 units

(c) 6.3 units

(d) More information is needed to determine the answer

3. Refer again to Fig. 2-6. Suppose we know that the measure of ∠BCA is 50° and the length of line segment AD is 5.3 units. What is the length of line segment A B? Express your answer to one decimal place (that is, the nearest tenth of a unit). Use a calculator if necessary.

(a) 6.9 units

(b) 8.2 units

(c) 6.3 units

(d) More information is needed to determine the answer

4. Suppose we have a right triangle, and the interior vertex angle at one end of the hypotenuse measures 30°. What is the measure of the interior vertex angle at the other end of the hypotenuse?

(a) π/3 rad

(b) π/4 rad

(c) π/6 rad

(d) More information is needed to determine the answer

5. Refer again to Fig. 2-6. Suppose we know that line segment AD is exactly 2/3 as long as line segment AB. What is the measure of ∠DAB ? Express your answer to the nearest tenth of a degree. Use a calculator if necessary.

(a) 33.7°

(b) 41.8°

(c) 48.2°

(d) 56.3°

6. Suppose, in reference to Fig. 2-6, we are told that the measure of ∠BCA is 50° and the measure of ∠ABC is 38°. We think that the person who says this must be mistaken because

(a) it would imply that Δ ABC is a right triangle, which is impossible

(b) it would imply that the measure of ∠CAD is something other than 40°, but it must be 40° to fulfill the rule that the sum of the measures of the interior angles of any triangle is 180°

(c) we know that the measure of ∠ABC is 40° because Δ ABC is an isosceles triangle

(d) of a rush to judgment! It is entirely possible that the measure of ∠BCA is 50° and the measure of ∠ABC is 38°

7. Suppose you are told that the sine of a certain angle is 0.5299, accurate to four decimal places, and the cosine of that same angle is 0.8480, also accurate to four decimal places. What is the sine of twice this angle, accurate to two decimal places? Don’t use the trigonometric function keys on your calculator to figure this out.

(a) 0.90

(b) 0.45

(c) 1.60

(d) 0.62

8. You are told that the sine of a certain angle is equal to –1.50. You can surmise from this that

(a) the angle has a measure greater than π/2 rad but less than π rad

(b) the angle has a measure greater than π rad but less than 3π/2 rad

(c) the angle has a measure greater than 3π/2 rad but less than 2 π rad

(d) either you didn’t hear the figure correctly, or else the person who told it to you is misinformed

9. Suppose there is a triangle whose sides are 6, 8, and 10 units, respectively. What, approximately, is the tangent of the angle θ opposite the side that measures 8 units?

(a) 0.600

(b) 0.750

(c) 1.333

(d) It is not defined

10. Suppose there is a triangle whose sides are 6, 8, and 10 units, respectively. What, approximately, is the secant of the angle θ opposite the side that measures 10 units?

(a) 0.600

(b) 0.750

(c) 1.333

(d) It is not defined

Answers:

1. b

2. a

3. d

4. a

5. c

6. d

7. a

8. d

9. c

10. d