Math 2412 Chapter 6 Notes Spring 2017.pdf

# Math 2412 Chapter 6 Notes Spring 2017.pdf - 6.1 Radian...

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128 6.1 Radian Measure Radian An angle with its vertex at the center of a circle that intercepts an arc on the circle equal in length to the radius of the circle has a measure of 1 radian. Unlike degrees, radians can be used to compute distance. y x Converting Between Degrees and Radians 1. Multiply a degree measure by 180 radians to convert to radians. 2. Multiply a radian measure by o 180 to convert to degrees. Caution: When no unit of angle measure is given, it is understood that the angle is measured in radians.
129 Convert each degree measure to radians. Leave answers as multiples of π. 565.8 30 o Solution radians o 180 30 30 rad rad 6 180 30 # 565.14 -315 o Solution LTR
130 565.44 264.9 o Solution LTR 565.46 174 o 50’ Solution LTR
131 Convert each radian measure to degrees. 565.26 3 8 Solution o 180 3 8 3 8 o o 480 3 1440 # 565.32 5 8 Solution LTR
132 Convert each radian measure to degrees. Write answers to the nearest minute. 565.54 5 Solution LTR 565.58 9.84763 Solution LTR
133 Arc Length The length s of the arc intercepted on a circle of radius r by a central angle of measure θ radians is given by s = rθ, where θ is measured in radians. Find the length to three significant digits of each arc intercepted by a central angle θ in a circle of radius r. 567.74 r = 0.892 cm, 10 11 rad Solution r s cm cm 08 . 3 10 11 892 . 0 # 567.78 r = 71.9 cm, θ = 135 o Solution LTR
134 Find the distance in kilometers between each pair of cities, assuming they lie on the same north-south line. 567.84 Farmersville, California, 36 o N, and Penticton, British Columbia, 49 o N. Solution LTR
135 567.89 Two gears are adjusted so that the smaller gear drives the larger one. If the smaller gear rotates through an angle of 300 o , through how many degrees will the larger gear rotate? Solution First, convert 300 o to radians. radians o 180 300 300 rad 3 5 . Now, we find the arc length of the smaller gear. r s . 30 185 3 5 . 18 3 5 7 . 3 cm cm cm An arc with this length on the la rger gear corresponds to an angle θ, where s = rθ. Now, we find θ for the larger gear. 1 . 7 30 185 r s 213 185 . Now, we convert θ to degrees.
136 o o 71 11100 180 213 185 . 156 o # Area of a Sector The area A of a sector of a circle of radius r and central angle θ is given by 2 2 1 r A , θ in radians. Find the area of a sector of a circle having radius r and central angle θ. Express answers to the nearest tenth. 569.16 r = 90.0 km, θ = 270 o Solution First, we convert 270 o to radians. radians o 180 270 270 rad 2 3 .

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