ANGLES & RADIAN MEASURE MATH 1113 SECTION 4.1 CREATED BY LAURA RALSTON

“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 17 th 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 ( , , or  )

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 Generated by counterclockwise rotation NEGATIVE ANGLES Generated by clockwise rotation

ANGLE LIES IN A QUADRANT Terminal side of angle in standard position lies in a quadrant Examples QUADRANTAL ANGLE Terminal side of angle lies ON the x-axis or y-axis Examples

MEASURE OF ANGLES AMOUNT OF ROTATION FROM THE INITIAL SIDE TO THE TERMINAL SIDE DEGREES, ° 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 2  ≈6.28

RELATIONSHIP (CONVERSION) BETWEEN DEGREES AND RADIANS DEGREES TO RADIANS RADIANS TO DEGREES

ANGLES ARE CLASSIFIED BY DEGREES OR RADIANS ACUTE ANGLERIGHT ANGLE

ANGLES ARE CLASSIFIED BY DEGREES OR RADIANS OBTUSE ANGLE STRAIGHT ANGLE (LINE) Measures exactly 180 ° or   °  

COTERMINAL ANGLES

LENGTH OF A CIRCULAR ARC Let r be the radius of a circle and  the nonnegative radian measure of a central angle of the circle  The length of the arc intercepted by the central angle is s = r  Draw picture Examples

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