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Chapter 3 Radian Measure and Circular Functions

By Sylvia Ward,2014-08-09 00:20
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Chapter 3 Radian Measure and Circular Functions

    Chapter 3, Section 3.1 Radian Measure

    There are several different ways to measure angles, just as there are different ways to measure length. One way to measure angles is in radians, and it is

    especially useful in advanced mathematics.

Radian

    ; The measure of a central angle θ that intercepts

    an arc s equal in length to the radius r of the

    circle.

    s

    

    r

    What is the radian measure of the entire unit circle?

    Converting Between Degrees and Radians

    360 = 2 radians or 180 = radians

    180

    1 = radians, or 1 radian =

    180

Conversion:

    180

    1. Multiply a radian measure by and simplify to

    

     convert to degrees.

    

    2. Multiply a degree measure by and simplify

    180

     to convert to radians.

Example: Convert each degree measure to radian.

    a. 45 b. 30 c. 210

    d. 720 e. 249.8 f. 5340’

    Example: Convert each radian measure to degrees.

    92

     b. c. a.

    452

    3

    d. e. 4.25 f. -3.2

    2

    Finding Function Values for Angles in Radians

    Example: Find each of the following functions:

    2π4π

    a. tan = ________ b. csc = __________

    33

    3ππ,(,(c. cot= ________ d. sin;= ________ ;!;!;

    43,,,,

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