Section 4 1 Radian and Degree Measure Angles

Angles �Trigonometry: the measurement of angles �Standard Position: Angles whose initial side is on

Graphing positive angles 1. ) 50º 2. ) 130º 3. ) 260º 4. )

Graphing Negative angles (go back to graph and write in) 1. ) -50º 2.

Coterminal angles �Angles that share the same terminal side �Differ by 360º (or a

Radian Measure �Radians are a 2 nd way to measure an angle �Positive and

Graphing positive angles 1. ) 2. ) 3. ) 4. )

Graphing negative angles 1. ) 2. ) 3. ) 4. )

Coterminal angle with radians �Differ by �To find a positive and negative coterminal angle,

Conversions �Degree to radian: Multiply by �Radian to degree: Multiply by 1. ) 2.

Special angles �Complementary angles- angles whose sum = 90 �Supplementary angles- angles whose sum

DMS �A degree, represented by the symbol °, is a unit of angular measure

Working with DMS measure �Convert 37. 425° to DMS. �Convert 42° 24’ 36” to

Arc Length �Arc length- measures a segment (arc) of a circle � must be

Arc Length Degree Measure Find the length of an arc that subtends a central

Angular and Linear Speed �Angular speed is measured in units like revolutions per minute.

Angular Speed �Jaxen’s truck has wheels 36 inches in diameter. If the wheels are

Homework �Page 265 -268 11 -19 odd, 40 -46 even, 59 -69 odd, 81

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Section 4. 1 Radian and Degree Measure

Angles �Trigonometry: the measurement of angles �Standard Position: Angles whose initial side is on the positive x-axis terminal vertex initial 90º 0º 180º 270º

Graphing positive angles 1. ) 50º 2. ) 130º 3. ) 260º 4. ) 310º

Graphing Negative angles (go back to graph and write in) 1. ) -50º 2. ) -180º 3. ) -240º 4. ) -300º

Coterminal angles �Angles that share the same terminal side �Differ by 360º (or a multiple of 360 ie. 720) �Example 4 vs example 1 �To find positive and negative coterminal angles- add and subtract 360º � 1. ) 210º 2. )-180º 3. ) 400º

Radian Measure �Radians are a 2 nd way to measure an angle �Positive and negative radian measures:

Graphing positive angles 1. ) 2. ) 3. ) 4. )

Graphing negative angles 1. ) 2. ) 3. ) 4. )

Coterminal angle with radians �Differ by �To find a positive and negative coterminal angle, add and subtract 1. ) 2. ) 3. )

Conversions �Degree to radian: Multiply by �Radian to degree: Multiply by 1. ) 2. ) 3. )

Special angles �Complementary angles- angles whose sum = 90 �Supplementary angles- angles whose sum = 180 1. ) 45º 2. ) 61º 3. ) 100º

DMS �A degree, represented by the symbol °, is a unit of angular measure equal to 1/180 th of a straight angle. In the DMS (degree-minutesecond) system of angular measure, each degree is subdivided into 60 minutes (denoted by ‘) and each minute is subdivided into 60 seconds (denoted by “).

Working with DMS measure �Convert 37. 425° to DMS. �Convert 42° 24’ 36” to degree.

Arc Length �Arc length- measures a segment (arc) of a circle � must be in radians � 1. ) 2. )

Arc Length Degree Measure Find the length of an arc that subtends a central angle with measure 120 degrees in a circle with a radius of 5 inches.

Angular and Linear Speed �Angular speed is measured in units like revolutions per minute. �Linear speed is measured in units like miles per hour.

Linear Speed

Angular Speed �Jaxen’s truck has wheels 36 inches in diameter. If the wheels are rotating at 630 rpm (revolutions per minute), find the trucks speed in miles per hour.

Homework �Page 265 -268 11 -19 odd, 40 -46 even, 59 -69 odd, 81 -84 all, 96, 99