Review the following concepts if needed:

**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

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

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