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Circles: Degrees and Radians This is an animation of one "radian". A complete circle has degrees Type in the missing degrees. º º A circle has 360 degrees. Type in the missing degrees. º 240º º 300º 60º 0º, 360º It takes 2π radii (about 6.28 radii) to travel a full circle. The circumference of a circle is Recall: C=2πr If 2π radii are needed for a circle, 1π radii would wrap around half ? C=2πr It takes 2π radii to travel a full circle. full ? a circle. What is a "radian"? An angle of 1 radian cuts off an arc equal to 1 radius. An angle of 2π radians creates a full circle. 2π radians = degrees 1π radian = degrees 180 ? 360 ? Drag each radian measureto the correctlocation onthe circle. π ? 3π 2 ? π2 ? 0 rad 2π rad A full circle has 2π radians. Drag the correct values to show the radian measure of the missing angles. π ? 2π 3 4π 3 5π 3 ? π3 ? 0 rad 2π rad Simplify the fraction. Your answer should be in terms of π. You can use a conversion factor to convert any angle in degrees to the equivalent radian measure. An example is shown to convert 100º to radians. 100º 1 × 100º = π rad180º 5π 9 = radians 100π 180 radians Convert 120º to radians. Simplify your answer. 120º 1 × π rad180º ? = 120º = 120π180 ? π rad Convert 70º to radians. Simplify your answer. 70º 1 × π rad180º ? = 70º = 70π180 ? π rad The π's will cancel out of the numerator and denominator. Simplify the fraction. You can use a conversion factor to convert any angle in radians to the equivalent degree measure. An example is shown to convert 3π radians to degrees. 3π rad 5 540 5 × 180º π rad = 108º = 5 540º 5 Convert 5π radians to degrees. Simplify your answer. 5π rad 6 6 × 180ºπ rad ? = 5π rad 6 900 6 ? º = º Convert 3π radians to degrees. Simplify your answer. 3π rad 2 2 × 180ºπ rad ? = 3π rad 2 540 2 ? º = º |