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TRIGONOMETRY HOMEWORK

23.

Convert the angle in radians to degrees

 


24.

Convert the angle in radians to degrees.

 

(Simplify your answer.)

25.

Convert the angle in degrees to radians.
5
°

 

radian(s)
(Round to two decimal places as needed.)

26.

Convert the angle in degrees to radians.
-20
°

 

radian(s)
(Round to two decimal places as needed.)

27.

Convert the angle in degrees to radians.
141
°

 

radian(s)
(Simplify your answer. Round to two decimal places as needed.)

28.

Convert the angle in radians to degrees.
3.23

 

(Round to two decimal places as needed.)

29.

Convert the angle in radians to degrees.
10

 


(Simplify your answer. Round to two decimal places as needed.)

30.

Convert the angle in radians to degrees. Ex press your answer in decimal form.
4.07

 

(Round to two decimal places.)

31.

Find the length s of the arc of a circle of radius centimeters subtended by the central
angle 1/3 radian.

 


32.

s denotes the length of the arc of a circle of radius r subtended by the central angle .
Find the missing quantity.
θ =1/2 radian, s = 3 feet, r =?

 

The radius of the circle is feet. (Simplify your answer.)

33.

Find the central angle θ which subtends an arc of length 15 miles of a circle of radius
21 miles.

 

(Round to six decimal places as needed.)
Convert to degrees.
(Round to three decimal places as needed.)

34.

Find the length s of the arc of a circle of radius 20 feet subtended by the central angle
78
°.

 

(Round to three decimal places.)

35.

Find the area A of the sector of a circle of radius 20 miles formed by the central angle
1/10 radian.

 

(Round to three decimal places.)

36.

Find the radius of a circle which has a sector of area 21 square feet de termined by a
central
angle 1/3 radian.

 

(Round to three decimal places.)

37.

Find the length s and area A.

 


(Round to three decimal places as needed.)


(Round to three decimal places as needed.)


38.

Find the length s and area A.

 

The length of the arc is yards.
(Round to three decimal places as needed.)
The area A of the sector is square yards.
(Round to three decimal places as needed.)

39.

The minute hand of a clock is 5 inches long. How far does the tip of the minute hand
move in 20 minutes?

 

inches (Round to three decimal places.)

40.

A water sprinkler sprays water over a distance of 20 feet
while rotating through an angle of 125
°. What area of lawn
receives water?

 

The area A of the sector is square feet.
(Round to two decimal places as needed.)

41.

An object is traveling around a circle with a radius of 10 inches. If in 50 seconds a
central angle of 1/4 radian is swept out, what are the linear and angular speeds of the
object?

 

The linear speed of the object is
  (Round to three decimal places.)
The angular speed of the object is
(Round to three decimal places.)

42.

The diameter of each wheel of a bicycle is 28 inches. If you are traveling at a speed of
15 miles per hour on this bicycle, through how many revolutions per minute are the
wheels turning?

 

(Round to one decimal place.)

43.

City A is due north of City B. Find the distance between City A ( 37°2' north latitude)
and City B (19
°38' north latitude). As sume that the radius of Earth is 3960 miles.

 

The distance between City A and City B is miles.
(Round to the nearest mile as needed.)

44.

A planet rotates on an axis through its poles and 1 revolution takes 1 day (1 day is 26
hours). The distance from the axis to a location on the planet 30
° north latitude is about
2253.5 miles. Therefore, a location on the planet at 30
° north latitude is spinning on a
circle of radius 2253.5 miles. Compute the linear speed on the surface of the planet at
30
° north latitude.

 

The linear speed on the surface of the planet is miles/hr.
(Round the final answer to the nearest integer as needed. Round all intermediate values
to five decimal places as needed.)

45.

To approximate the speed of the current
of a river, a circular p addle wheel with
radius 6 ft. is lowered into the water . If
the current causes the wheel to rotate at a
speed of 20 revolutions per minute, what
is the speed of the current?

 

The speed of the current is
(Round to two decimal places.)

46.

At a museum you can see the four cable lines that are used to pull cable cars up and
down a hill. Each cable travels at a speed of 9.45 miles per hour, caused by a rotating
wheel whose diameter is 7.5 feet. How fast is the wheel rotating? Express your answer
in revolutions per minute.

 

The angular speed of the wheel is rev/min.
(Round to two decimal places as needed.)
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