Angle Measure
Find the angle of least positive measure coterminal with the given angle.
1332o
252o
In which two quadrants is the value of tangent negative?
II and IV
Find the exact value of cos(-2𝝅/3).
-½
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
Find the angular velocity if 𝜽=𝝅/6 radians and t=11 seconds.
Answer in terms of 𝝅.
𝝅/66 radians per second
Convert the angle to decimal degrees and round to the nearest hundredth of a degree.
312° 43′ 42′′
312.73°
If sintheta=-2/3 and tantheta<0 , in which quadrant does thee endpoint lie?
IV
Find the exact value of tan(5𝝅/3).
-sqrt3
Find the area of a sector of a circle with radius r=7.4mi and central angle 𝜽=314o.
Round to the nearest tenth.
150.1 mi2
Find the angular velocity if v=12 ft/s and r=1.6 ft.
7.5 radians per second
Convert 38.80o to radians.
Round to four decimal places.
0.6772
sectheta<0 and tantheta=-9/17
Name the quadrant.
II
Find the exact value of
csc(315o).
-sqrt2
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
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
Convert 0.8996 radians to degrees.
Round to the nearest hundredth.
51.54o
If sintheta=-12/37 and costheta<0 , find tantheta .
12/35
Find the value of 𝚹 on the interval 0<𝚹<𝝅 that makes this statement true:
cos 𝚹 = -½
(2pi)/3
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?
147.3o
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
Through how many radians will the hour hand of a clock rotate in 15 hours?
Answer in terms of 𝝅.
2.5𝝅
The point (8,-1) is a point on the terminal side of theta in standard form. Find the exact value of
csctheta.
-sqrt65
Find the exact value of s in the interval (3pi)/2<s<2pi that makes this statement true:
tans=-sqrt3/3
(11pi)/6
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
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