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Published byPercival Summers Modified over 9 years ago
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Objectives Change from radian to degree measure, and vice versa Find angles that are co-terminal with a given angle Find the reference angle for a given angle
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Angles and Their Measures Angles are formed by the rotation of two rays that share a common and fixed endpoint. If one ray remains fixed, it forms the initial side. The second ray rotates to form the terminal side. If the rotation is in a counter-clockwise direction, it forms a positive angle. If the rotation is in a clockwise direction, it forms a negative angle. An angle that has its vertex at the origin and its initial side along the x-axis, the angle is said to be in standard position.
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The angles below are all in standard position Positive angle Initial side Terminal side Negative angle Initial side Terminal side Quadrantal Angle Initial Side Terminal Side
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Angle Measurement There are two common units used to measure angles, degrees and radians. An angle is 1° if it is 1/360 of a revolution in the positive direction. Each degree consists of 60 minutes – 60’. Each minute consists of 60 seconds – 60”.
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Change 29°45’26” to a decimal number of degrees to the nearest one thousandth 29° + 45’(1/60) + 26”(1/3600) = 29° +.750° +.007° = 29.757°
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Radians Another unit of measure is the radian. The definition of a radian is based on the unit circle. A unit circle is a circle with a radius of 1. There is an important relationship between degrees and radians. Since one revolution of a circle is either 360° or 2 radians: 360° = 2 radians 180° = radians 90° = /2 radians 45° = /4 radians
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Degree/Radian Conversion Formulas To change degrees to radians: multiply by /180 radians To change radians to degrees: multiply by 180°/ 1 radian = about 57.3° 1 degree = about 1.017 radians
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Assignment Make a unit circle with multiples of 30° –Label both degree and radian measures Make a unit circle with multiples of 45° -- label both degree and radian measures Tomorrow - co-terminal angles and reference angles
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