University:
Felician University
Course:
MATH-231 | Geometry I
Academic year:

2021
Views:

97

Pages:

27
Author:

do3ran7ut

What I Need to Know OBJECTIVES After going through this lesson, you are expected to: illustrate the unit circle and the relationship between the linear and angular measures of arcs in a unit circle. convert degree measure to radian measure, and vice versa. illustrate angles in standard position and coterminal angles. MEASURES OF ARCS IN A UNIT CIRCLE What's In REVIEW ANGLE MEASURE An angle is formed by rotating a ray about its endpoint. P Q MEASURES OF ARCS IN A UNIT CIRCLE What's In REVIEW ANGLE MEASURE A42 Radian measure allows us +1 to treat the trigonometric functions as functions with the set of real numbers as domains, angles. rather than 1 P 0 0 +-1 B-2 MEASURES OF ARCS IN A UNIT CIRCLE What's In REVIEW ANGLE MEASURE A central angle of the unit circle that intercepts an arc of the circle with length 1 unit is said to have a measure of one radian, written 1 rad. Ty 1 radian ≈ 57.3° X MEASURES OF ARCS IN A UNIT CIRCLE What's In REVIEW ANGLE MEASURE MEASURES OF ARCS IN A UNIT CIRCLE What's New ICE BREAKER ANGLE MEASURE A unit circle has circumference 2pi a central angle that measures 360 deg has measure equivalent to 2pi radians. Thus, we obtain the following conversion rules. To convert a degree measure to radian, multiply it by pi/180 To convert a radian measure to tiply it by 180/pi degree, multiply it by 120 deg = (2pi)/3 135 deg = (3pi)/4 150 deg = (5pi)/6 180 deg = pi 210 deg = (7pi)/6 225 deg = (5pi)/4 240 deg = (4pi)/3 90 deg = pi/2 60 deg = pi/3 45 deg = pi/4 30 deg = pi/6 0 deg = 0 360 deg = 2pi 330 deg = (11pi)/6 315 deg = (7pi)/4 300 deg = (5pi)/3 270 deg = (3pi)/2 MEASURES OF ARCS IN A UNIT CIRCLE What's New ICE BREAKER EXAMPLE: 1. Convert the following degree measures to radian measure. (a) 60° (b) 90° (c) 150° 2. Convert the following radian measures to degree measure. (a) rad (b) rad MEASURES OF ARCS IN A UNIT CIRCLE What is It DISCUSSION COTERMINAL ANGLES YA Angles in standard position whose terminal sides coincide are called coterminal angles. 405° These angles are not necessarily equal. Degree measures of coterminal angles differ by multiples of 360°. -315° 45° Initial Side X