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Find the radian measure of the central angle of a circle with ---

By Jeanne Smith,2014-08-09 04:04
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Find the radian measure of the central angle of a circle with ---

Trigonometry Name: ____________________

    Chapter 3.2 Worksheet Per: ___ Date: ______________

On a circle of radius r, find the length of the arc s intercepted by the central angle θ.

     Radius Central Angle Central Angle (in radians) Arc Length (units)

    1. 15 inches 180 degrees ______________ ______________ 2. 9 feet 60 degrees ______________ ______________ 3. 6 meters 2 radians ______________ ______________ 4. 40 centimeters 135 degrees ______________ ______________

    Find the radian measure of the central angle of a circle with radius r that intercepts an arc of length s.

     Radius Arc Length Radian Measure

    5. 15 inches 4 inches ______________

    6. 16 feet 10 feet ______________

    7. 14.5 centimeters 25 centimeters ______________ 8. 80 kilometers 160 kilometers ______________

Find the distance between the two cities of given latitudes, assuming that the earth is a sphere of

    radius 4,000 miles and that the cities are on the same meridian (one city is due north of the other).

    09. Dallas, TX 32 47’ 09” N Omaha

    0 Omaha , NE 41 15’ 42” N 4,000 miles

     Dallas 4,000 miles

     Jerusalem 10. Find the distance between the two cities of given

    latitudes, assuming that the earth is a sphere of

    radius 4,000 miles and that the cities are on the same

    4,000 miles meridian (one city is due north of the other).

    Specifically, find the distance between Jerusalem,

    0 47’ N and Johannesburg, South Africa Israel, at 31

    0at 26 10’ S, where N designates the Northern

    Hemisphere and S designates the Southern

    Hemisphere.

     4,000 miles

     Johannesburg

    011. A pendulum of length 17.6 inches swings 1 15’ to each side of its vertical position. What is

    the length of the arc through which the end of the pendulum swings?

13. A bicycle with a 26 inch diameter wheel travels a distance of 700 feet. How many

    revolutions does the wheel make, to the nearest revolution?

    0 determines a sector area of 42 14. Find the radius of a circle in which a central angle of 36

    square meters.

    15. What is the difference in area covered by a single 5-inch windshield wiper operating with a

    0central angle of 136 compared to a pair of 2-inch wipers operating together, each having a

    0central angle of 120?

    16. Two wheels are rotating in such a way that the rotation of the smaller 20.9 cm wheel causes the larger wheel to rotate. The radius of the smaller

    4.4 cm wheel is 4.4 centimeters, while the radius of the larger wheel is 20.9

    centimeters. Through how many degrees will the larger wheel rotate

    0if the smaller one rotates through 89?

    ;;345501),47.12in.2),9.42ft.3)2rad.,12meters4),94.25cm5)6)7)8)2rad. 3415829

    209)591.72miles10)4,045.70miles11)1.31"12)Approx.103rev.13)r11.5614)Diff.25.48in.15)18.74;;?;

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