University:
Missouri State University
Course:
MTH 460 | College Geometry
Academic year:

2022
Views:

140

Pages:

10
Author:

Avery Benjamin

CENTRAL ANGLES ANGLE: Two rays with the same endpoint CENTRAL ANGLE: An angle with its endpoints located at the origin of the coordinate plane INITIAL SIDE: Ray that will ALWAYS lie on the positive x-axis TERMINAL SIDE: Other ray that has the same endpoint as the initial side CENTRAL ANGLES INITIAL SIDE TERMINAL SIDE CENTRAL ANGLES POSITIVE ANGLE counter clockwise NEGATIVE ANGLE clockwise EXAMPLE 1, Measuring angles in degrees a.) 180° b.) 360° c.) 90° d.) 270° MEASURING ANGLES IN DEGREES 90 ^ n < 0 < 180 ^ n QUADRANTI QUADRANT II EXAMPLE 2: Measuring angles in degrees a.) 25 deg b.) 250 deg 1800270 270 deg < 0 < 160 deg QUADRANT III QUADRANT IV с.) 100 deg d.) 285 deg EXAMPLE 3: Measuring angles in degrees a.) - 125 deg b.) - 230 deg c) - 50 deg d.) - 335 deg WHAT ARE RADIANS? 5 A RADIAN, 0, is the measure of a central angle 70 It is equal to the ratio of the length of intercepted arc, s, and the length of the radius. theta = s/r HOW MANY RADIANS ARE IN A CIRCLE? T S We know there are 360 degrees in a circle in an entire circle, the arc length, s, we are interested in, would be equal to the circumference of the circle IC = 2pi*r HOW MANY RADIANS ARE IN A CIRCLE? theta = 5/r theta = (2pi*r)/r theta = 2pi Therefore; There are 21t radians in a circle Which means... HOW MANY RADIANS ARE IN A CIRCLE? 2pi RADIANS = 360 deg EXAMPLE 4: Measuring angles in radians a.) π b.) 2pi pi/2 d.) (3pi)/2