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# Note for MATH 1330 at UH

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This 7 page Class Notes was uploaded by an elite notetaker on Friday February 6, 2015. The Class Notes belongs to a course at University of Houston taught by a professor in Fall. Since its upload, it has received 14 views.

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Date Created: 02/06/15

Another principal means of measuring the size of an angle is using radian measure Begin with a circle of radius r and let 9 be a central angle an angle whose vertex is the center of the circle Lets be the length of the arc that is intercepted by the angle The radian measure of 6 is given by 6 3 where r and s have the same linear units r Example 1 A circle has a radius of 9 inches A central angle 9 intercepts an arc of length 36 inches What is the radian measure of 6 7 Example 2 A circle has a radius of 24 inches A central angle 9 intercepts an arc of length 7 feet What is the radian measure of 6 To deVise a formula for converting between degree measure and radian measure consider the right angle shown in the figure below Since 6 measures 90quot the arc length s is 14 the circumference of the circle 1 727 S 2727 4 2 727 Use the formula for radian measure and substitute 7 for S 727 9232221 F r 2 Therefore 90quot gradians To obtain formulas for converting between degree measure and radian measure multiply both sides of the equation above by 2 180 7 radium 180 From the formula above we see that 10 radlans z 0017 rad1anand lradlan z 5730 7r 7239 To convert from degree measure to radian measure multiply degrees by 1800 180 7239 To convert from radian measure to degree measure multiply radians by Common Angles 30 1 90 1 6 2 45 1 180 7r 4 60 2 360 27 Memorize the common angles Example 3 If two angles of a triangle have radian measures 27 and find the radian measure of the third angle Example 4 Convert the following degree measure to radians 300 Example 5 Convert the following degree measure to radians 500 Example 6 Convert the following radian measure to degrees 7 7r 4 Example 7 Convert the following radian measure to degrees 7239 l 2 In a circle of radius r the arc length s that is determined by a central angle of radian measure 9 is given by the arc length formula S 9 where r and s have the same linear units In a circle of radius r the area A of a sector with central angle of radian measure 6 is given by the 1 area sector formula A r29 47 Example 8 Find the radius of a circle if the length of the intercepted arc by a central angle 3 15 397 inches 7239 Example 9 Find the sector area determined by a circle that has a radius of 5 cm and central angle ftz Find the radius of the 8 Example 10 A sector of a circle has a central angle 1350 and area circle Math 1 3 30 Section 42 Radian Arc Length and Area of a Sector An angle is formed by two rays that share a common endpoint called the vertex of the angle The vertex can represent a point of rotation in that one ray is the initial side of the angle before rotation and the other ray forms the terminal side after the rotation Terminal side Vertex Initial side One principal means of measuring the size of an angle is using degree measure An angle formed by the rotation of a ray through one complete circle measures 360 degrees

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