Unit 3 - Radian Measure & The Unit Circle

Angle Measure

100

Find the angle of least positive measure coterminal with the given angle.

1332^o

252^o

200

Convert the angle to decimal degrees and round to the nearest hundredth of a degree.

312° 43′ 42′′

312.73°

300

Convert 38.80o to radians.

Round to four decimal places.

0.6772

400

Convert 0.8996 radians to degrees.

Round to the nearest hundredth.

51.54^o

500

Through how many radians will the hour hand of a clock rotate in 15 hours?  

Answer in terms of 𝝅.

2.5𝝅

Trig Functions at Any Angle

100

In which two quadrants is the value of tangent negative?

II and IV

200

If  sintheta=-2/3 and  tantheta<0 , in which quadrant does thee endpoint lie?

IV

300

sectheta<0 and tantheta=-9/17 

Name the quadrant.

II

400

If  sintheta=-12/37 and costheta<0 , find  tantheta .

12/35

500

The point (8,-1) is a point on the terminal side of  theta  in standard form.  Find the exact value of 

csctheta.

-sqrt65

The Unit Circle

100

Find the exact value of cos(-2𝝅/3).

-½

200

Find the exact value of tan(5𝝅/3).

-sqrt3

300

Find the exact value of 

csc(315^o).

-sqrt2

400

Find the value of 𝚹 on the interval 0<𝚹<𝝅 that makes this statement true:

 cos 𝚹 = -½ 

(2pi)/3

500

Find the exact value of s in the interval  (3pi)/2<s<2pi  that makes this statement true:

tans=-sqrt3/3

(11pi)/6

Arcs & Sectors

100

Find the length of the arc intercepted by angle 𝜽=𝝅/5 radians in a circle of radius r=49.97ft.

Round to the nearest tenth. 

31.4 ft

200

Find the area of a sector of a circle with radius r=7.4mi and central angle 𝜽=314^o.

Round to the nearest tenth.

150.1 mi²

300

Find the distance between City E, 15° N and City F, 65° S. Assume the cities lie on the same N-S line and the radius of the earth is 6400 km.

Round to the nearest kilometer.

8936 km

400

A car wheel has a 28 inch diameter.  Through what angle (to the nearest tenth of a degree) does the wheel turn when the car rolls forward 3 feet?

147.3^o

500

A center-pivot irrigation system waters a sector-shaped field. Find the area of the field ifthe central angle, θ = 44° and the radius, r = 148 meters. 

Round to the nearest whole number.

8411 m²

Circular Motion

100

Find the angular velocity if 𝜽=𝝅/6 radians and t=11 seconds.

Answer in terms of 𝝅.

𝝅/66 radians per second

200

Find the angular velocity if v=12 ft/s and r=1.6 ft.

7.5 radians per second

300

The radius of the tires of a car is 16 inches, and they are revolving at the rate of 539 rpm. How fast is the car traveling in miles per hour?

Round to the nearest tenth.

51.3 mph

400

Two pulleys of diameters 9 m and 3 m are connected by a belt. The larger pulley rotates 40 times per min. Find the angular speed in radians per minute of the smaller pulley.

Answer in terms of 𝝅.

240𝝅 radians per minute

500

A pulley with a diameter of 26 inches is driven by a belt which is moving 859 ft/min. To the nearest unit, how many revolutions per minute are made by the pulley?

126 rpm