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Pre Calculus 4.1 Radian and Degree Measure Name _________________________ Date ____________________ Trigonometry – “The measurement of triangles” The study of angular, rotational and periodic behavior and its application to problem solving as functions. Angles in the Coordinate Plane An angle is formed from the intersection of two rays. B O O ____________ OA _______________ A OB ___________________ An angle with its vertex at the origin and its initial side on the x-axis is said to be in ________________ position. Positive angles are formed by ________________ rotations. Measuring Angles Degrees and Radians Negative angles are formed by _________________ rotations. One degree is the angle formed by an arc equal to 1 th of a circle. 360 One radian is the angle formed by an arc equal to the radius of the circle. Radian measures give the ratio of the arc and the radius of the full circle. Conversions Co-terminality Angles with the same standard position, regardless of the direction or number of rotations of the terminal side are called co-terminal angles. Co-terminal angles are always of the form n360 or n2 where n is a positive or negative integer representing the direction and number of rotations. Exercises: Convert the following to the opposite angle measure: a. 80 b. -144 d. 9 2 e. 5 12 c. 420 f. 7 9 Give two co-terminal angles for the following (one positive and one negative) 5 a. 250 b. c. 2 3 4 90° 180° 360° 270° 90° 180° 360° 270°