Exam Name___________________________________

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Convert the degree measure to radians. Leave answer as a multiple of . 1) 30° Answer:

1)

6

Objective: (3.1) Convert Degrees to Radians (Exact)

2) -450° Answer: -

2)

5 2

Objective: (3.1) Convert Degrees to Radians (Exact)

Convert the radian measure to degrees. Round to the nearest hundredth if necessary. 3) -

3)

5

Answer: -36°

Objective: (3.1) Convert Radians to Degrees (Multiples of )

Convert the degree measure to radians. Leave answer as a multiple of . 4) 650° Answer:

65 18

Objective: (3.1) Convert Degrees to Radians (Exact)

1

4)

Convert the radian measure to degrees. Round to the nearest hundredth if necessary. 10 5) 3

5)

Answer: 600°

Objective: (3.1) Convert Radians to Degrees (Multiples of )

Convert the radian measure to degrees. Give answer using decimal degrees to the nearest hundredth. Use 3.1416 for . 6) 0.2521 6) Answer: 14.44°

Objective: (3.1) Convert Radians to Degrees (Not Multiples of i)

7) 1

7)

Answer: 57.30°

Objective: (3.1) Convert Radians to Degrees (Not Multiples of i)

Find the exact value without using a calculator. 2 8) cos 3 Answer: -

8)

1 2

Objective: (3.1) Evaluate Trig Function (Exact)

2

9) tan

-5 6

Answer:

9)

3 3

Objective: (3.1) Evaluate Trig Function (Exact)

10) sec

-5 4

10)

Answer: - 2

Objective: (3.1) Evaluate Trig Function (Exact)

11) csc

4 3

Answer: -

11)

2 3 3

Objective: (3.1) Evaluate Trig Function (Exact)

12) cot

-5 6

Answer:

12)

3

Objective: (3.1) Evaluate Trig Function (Exact)

3

Find the corresponding angle measure in radians. 13) 270°

Answer:

13)

3 2

Objective: (3.1) Give Radian Measure of Angle from Graph

Solve the problem. 14) Through how many radians will the hour hand on a clock rotate in 36 hours?

14)

Answer: 6

Objective: (3.1) Solve Apps: Radian Measure

Find the length of an arc intercepted by a central angle 15) r = 38.81 ft;

=

3

in a circle of radius r. Round your answer to 1 decimal place.

radians

15)

Answer: 40.6 ft

Objective: (3.2) Find Arc Length

Assume that the cities lie on the same north-south line and that the radius of the earth is 6400 km. 16) Find the distance between City A, 60° N and City B, 35° N. (Round to the nearest kilometer.) Answer: 2793 km

Objective: (3.2) Find Distance Between Cities/Latitude of City

4

16)

17) Find the latitude of Winnipeg, Canada if Winnipeg and Austin, TX, 30 °N, are 2234 km apart.

17)

Answer: 50 °N

Objective: (3.2) Find Distance Between Cities/Latitude of City

Solve the problem. 18) A pendulum swinging through a central angle of 78° completes an arc of length 6.4 cm. What is the length of the pendulum?

18)

Answer: 4.70 cm

Objective: (3.2) Solve Apps: Arc Length

19) A bicycle with a 24-inch wheel (diameter) travels a distance of 1000 feet. How many revolutions does the wheel make (to the nearest revolution)?

19)

Answer: 159 revolutions

Objective: (3.2) Solve Apps: Arc Length

20) A car wheel has a 16-inch radius. Through what angle (to the nearest tenth of a degree) does the wheel turn when the car rolls forward 2 ft? Answer: 85.9°

Objective: (3.2) Solve Apps: Arc Length

5

20)

Find the area of a sector of a circle having radius r and central angle . Express the answer to the nearest tenth. 21) r = 20.0 m, = 20° 21) Answer: 69.8 m2

Objective: (3.2) Find Area of Sector

Find the exact circular function value. 3 22) sin 4 Answer:

22)

2 2

Objective: (3.3) Evaluate Circular Function (Exact)

Use a table or a calculator to evaluate the function. 23) csc 0.2142

23)

Answer: 4.704

Objective: (3.3) Evaluate Circular Function (Approximate)

6

The figure shows an angle in standard position with its terminal side intersecting the unit circle. Evaluate the indicated circular function value of . 24) Find sin . 24) -

Answer:

5 12 , 13 13

12 13

Objective: (3.3) Find Circular Function Using Point on Unit Circle

25) Find tan . -

Answer: -

25) 5 12 , 13 13

12 5

Objective: (3.3) Find Circular Function Using Point on Unit Circle

7

26) Find tan .

26)

7 24 ,25 25

Answer: -

24 7

Objective: (3.3) Find Circular Function Using Point on Unit Circle

Find the value of s in the interval [0, /2] that makes the statement true. 27) tan s = 5.40368606

27)

Answer: 1.38780765

Objective: (3.3) Tech: Find Angle Given Decimal Function Value

Find the exact value of s in the given interval that has the given circular function value. 2 , ; sin s = 28) 2 2 Answer: s =

3 4

Objective: (3.3) Find Angle Given Exact Function Value

8

28)

29)

3 1 , 2 ; cos s = 2 2 Answer: s =

29)

5 3

Objective: (3.3) Find Angle Given Exact Function Value

Suppose an arc of length s lies on the unit circle x2 + y2 = 1, starting at point (1, 0) and terminating at the point (x, y). Use a calculator to find the approximate coordinates (x, y).

30) s = 3.1

30)

Answer: (-0.9991, 0.0416)

Objective: (3.3) Find Coordinates of Arc End Point Given Arc Length

For the given value of s, decide in which quadrant an angle of s radians lies by evaluating sin s and cos s. 31) s = 33 31) Answer: II

Objective: (3.3) Find Quadrant Given Arc Length

9

Use the formula 32)

=

=

10

t

to find the value of the missing variable.

radian per min, t = 13 min

Answer:

32)

13 radians 10

Objective: (3.4) Use Angular Speed Formula

Use the formula v = r to find the value of the missing variable. 33) v = 10 ft per sec, r = 1.3 ft

33)

Answer: 7.7 radians per sec

Objective: (3.4) Use Linear Speed Formula

Use the formula s = r t to find the value of the missing variable. 34) s =

3

m, r = 7 m, t = 4 sec

Answer:

84

34)

radian per sec

Objective: (3.4) Use Distance Formula

Solve the problem. 35) Two pulleys of diameters 6 m and 3 m are connected by a belt. The larger pulley rotates 35 times per min. Find the angular speed of the smaller pulley. Answer: 140 radians per min

Objective: (3.4) Solve Apps: Linear and Angular Speed

10

35)

36) The radius of the tires of a car is 18 inches, and they are revolving at the rate of 673 revolutions per minute. How fast is the car traveling in miles per hour? Answer:

2019 88

36)

mph

Objective: (3.4) Solve Apps: Linear and Angular Speed

37) An object is spinning around a circle with a radius of 16 centimeters. If in 13 seconds a 1 central angle of radian has been covered, what is the linear speed of the object? 6 Answer:

37)

8 cm per sec 39

Objective: (3.4) Solve Apps: Linear and Angular Speed

38) A ball on the end of a string is spinning around a circle with a radius of 5 centimeters. If in 1 5 seconds a central angle of radian has been covered, what is the angular speed of the 18 ball?

Answer:

1 radian per sec 90

Objective: (3.4) Solve Apps: Linear and Angular Speed

11

38)