“TRIGONOMETRY” Derived from Greek language Means “measurement of triangles” Initially, trig dealt with relationships among the sides and angles of triangles and was used in astronomy, navigation, and surveying In 17th century, a different perspective arose: trig relationships were viewed as functions of real numbers with applications including rotations and vibrations ANGLE Determined by rotating a ray about its endpoint Can be labeled with uppercase letters (A, B, or C) or with Greek letters (a, b, or q) ANGLE When viewed with respect to the coordinate system, an angle is in standard position if Its vertex is at the origin Its initial side lies along the positive x-axis ANGLE POSITIVE ANGLES N E G AT I V E A N G L E S Generated by counterclockwise rotation Generated by clockwise rotation ANGLE LIES IN A QUADRANT Q UA D R A N TA L A N G L E Terminal side of angle in standard position lies in a quadrant Terminal side of angle lies ON the x-axis or y-axis Examples Examples MEASURE OF ANGLES AMOUNT OF ROTATION FROM THE INITIAL SIDE TO THE TERMINAL SIDE DEGREES, ° Full rotation (revolution) = 360° 1 1° = of a rotation 360 about the vertex RADIANS Useful in calculus Measure of the central angle of a circle that intercepts an arc equal in length to the radius of the circle (draw picture) Full revolution is 2p≈6.28 RELATIONSHIP (CONVERSION) BETWEEN DEGREES AND RADIANS DEGREES TO RADIANS Multiply stated degrees by 180° RADIANS TO DEGREES Multiply stated radians 180° by Examples Examples ANGLES ARE CLASSIFIED BY DEGREES OR RADIANS ACUTE ANGLE RIGHT ANGLE Measures between 0° and 90° or between 0 radians and radians Measures exactly 90° or 2 0° < q < 90° 0<q< 2 2 q= 2 ANGLES ARE CLASSIFIED BY DEGREES OR RADIANS OBTUSE ANGLE STRAIGHT ANGLE (LINE) Measures between 90° and 180° or between radians and p 2 radians Measures exactly 180° or p 90° < q < 180° q= p 2 <q< p q = 180° COTERMINAL ANGLES Two or more angles with the same initial and terminal side, but possibly different rotations Every angle has infinitely many coterminal angles. ± 360°, ℎ ± 2, ℎ LENGTH OF A CIRCULAR ARC Let r be the radius of a circle and q the nonnegative radian measure of a central angle of the circle. The length of the arc intercepted by the central angle is s = rq Draw picture Examples ASSIGNMENT Page 472 #1-73 odd

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# Angles & Radian Measure - Georgia Highlands College