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Name: ________________________ Class: ___________________ Date: __________ ID: A Trigonometry - Arc Length with Angle Review Problem Set Short Answer 1. What is the radian measure of the smaller angle formed by the hands of a clock at 7 o’clock? 5. Kristine is riding in car 4 of the Ferris wheel represented in the accompanying diagram. The Ferris wheel is rotating in the direction indicated by the arrows. The eight cars are equally spaced around the circular wheel. Express, in radians, the measure of the smallest angle through which she will travel to reach the bottom of the Ferris wheel. 2. Convert 3 radians to degrees and express the answer to the nearest minute. 3. Express 260º in radian measure. 4. Express 3π radians in degrees. 4 6. An arc of a circle that is 6 centimeters in length intercepts a central angle of 1.5 radians. Find the number of centimeters in the radius of the circle. 1 Name: ________________________ ID: A 12. In a circle, a central angle intercepts an arc of 12 centimeters. If the radius of the circle is 6 centimeters, find the number of radians in the measure of the central angle. 7. Kathy and Tami are at point A on a circular track that has a radius of 150 feet, as shown in the accompanying diagram. They run counterclockwise along the track from A to S, a distance of 247 feet. Find, to the nearest degree, the measure of minor arc AS. 13. An arc of a circle measures 30 centimeters and the radius measures 10 centimeters. In radians, what is the measure of the central angle that subtends the arc? 14. In a circle whose radius is 2, a central angle intercepts an arc whose length is 6. What is the number of radians in the central angle of the arc? 8. The pendulum of a clock swings through an angle of 2.5 radians as its tip travels through an arc of 50 centimeters. Find the length of the pendulum, in centimeters. 1 radians at the center of a circle 4 intercepts an arc of 18 inches. Find the length of the radius in inches. 15. An angle of 2 9. In a circle with a radius of 3 centimeters, find, in centimeters, the length of an arc intercepted by a central angle of 2 radians. 10. In a circle, an arc of length 10 is intercepted by a 2 central angle of radian. Find the radius of the 3 circle. 11. In a circle of radius 8, find the length of the arc intercepted by a central angle of 1.5 radians. 2 ID: A Trigonometry - Arc Length with Angle Review Problem Set Answer Section SHORT ANSWER 1. ANS: 5π 6 5 10π 5π 2π ⋅ = = 12 6 12 PTS: 2 2. ANS: 3× 180 π REF: 061125a2 STA: A2.M.1 TOP: Radian Measure ≈ 171.89° ≈ 171°53′ . PTS: 2 KEY: degrees 3. ANS: 13π 9 REF: 011335a2 STA: A2.M.2 TOP: Radian Measure PTS: 2 KEY: radians 4. ANS: 135 REF: 018401siii STA: A2.M.2 TOP: Radian Measure PTS: 2 KEY: degrees 5. ANS: 5π . 4 REF: 018603siii STA: A2.M.2 TOP: Radian Measure PTS: 2 6. ANS: REF: 010421b STA: A2.M.1 TOP: Radian Measure REF: 010526b STA: A2.A.61 TOP: Arc Length 4. PTS: 2 KEY: radius 1 ID: A 7. ANS: 94. PTS: 4 KEY: angle 8. ANS: . . REF: 060531b STA: A2.A.61 TOP: Arc Length REF: 060626b STA: A2.A.61 TOP: Arc Length PTS: 2 KEY: arc length 10. ANS: 15 REF: 068514siii STA: A2.A.61 TOP: Arc Length PTS: 2 KEY: radius 11. ANS: 12 REF: 068618siii STA: A2.A.61 TOP: Arc Length PTS: 2 KEY: arc length 12. ANS: 2 REF: 068713siii STA: A2.A.61 TOP: Arc Length PTS: 2 KEY: angle 13. ANS: 3 REF: 089508siii STA: A2.A.61 TOP: Arc Length PTS: 2 KEY: angle 14. ANS: 3 REF: 019615siii STA: A2.A.61 TOP: Arc Length PTS: 2 KEY: angle 15. ANS: 8 REF: 080108siii STA: A2.A.61 TOP: Arc Length PTS: 2 KEY: radius REF: 060312siii STA: A2.A.61 TOP: Arc Length 20. PTS: 2 KEY: radius 9. ANS: 6 2