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Degrees and Radians Initial side – start side of angle Degrees and Radians Initial side – start side of angle

Degrees and Radians Initial side – start side of angle - PowerPoint Presentation

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Uploaded On 2020-06-16

Degrees and Radians Initial side – start side of angle - PPT Presentation

Terminal side end side of angle Standard position An angle whose initial side is on the positive xaxis Positive angles An angle in standard position that rotates counterclockwise Negative angles ID: 778778

angles angle quadrant radians angle angles radians quadrant coterminal find examples side supplementary complementary positive negative reference degrees answer

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Slide1

Degrees and Radians

Slide2

Initial side – start side of angle

Terminal side – end side of angleStandard position – An angle whose initial side is on the positive x-axis

Slide3

Positive angles

An angle in standard position that rotates counterclockwise

Slide4

Negative angles

An angle in standard position that rotates clockwise

Slide5

Coterminal

AnglesAngles that have the same terminal side

Slide6

Simplify the Angles:

http://www.mathopenref.com/trigangle.html

Slide7

Quadrants

Quadrant III

Quadrant I

Quadrant II

Quadrant IV

Slide8

Angles of the axes

What quadrant is it in (and sketch)?

Slide9

Variables you will see for angle measures

Slide10

Radian

: made by taking the radius and wrapping it along the arc (edge of the circle)

http://www.mathopenref.com/radians.html

Slide11

Slide12

Radians

Angle measures can also be expressed in radiansA radian is the ratio of the length of an arc to its radiusRadians are expressed in terms of = 180o

To change from degrees to radians, multiply by and reduce.

To change from radians to degrees, multiply by

Slide13

Radians continued

Radians can take 2 forms – an exact answer and an approximate decimal answerThe exact answer has a in it and it is the usual way to see radiansTo find an exact answer with your calculator, do not put the in the calculator, only write it in the answer

Slide14

Angles of the axes in radians

Examples – quadrant &

skecth

Slide15

Conversion Examples

Change from degrees to radiansChange from radians to degrees

Slide16

Coterminal

angles: http://www.mathopenref.com/coterminal.htmlYou add or subtract multiples of 360o (or 2π

) to find

coterminal

angles

Find 2

coterminal angles (one positive and one negative) for 35o

Find 2 coterminal angles (one positive and one negative) for -23o

Find 2

coterminal

angles (one positive and one negative) for

740

o

Slide17

Examples for radians

Find a positive and negative coterminal angle

Slide18

Complementary/Supplementary

Complementary angles add up to 90o (or π/2 for radians)

Supplementary angles add up to 180

o

(or

π

for radians)

Slide19

Examples

What angle is complementary/supplementary to 36o ?What angle is complementary/supplementary to 110o ?

Slide20

Examples - radians

What angle is complementary/supplementary to ?What angle is complementary/supplementary to ?

Slide21

Reference Angles

A reference angle is the acute angle that an angle makes with the x-axis

Slide22

Finding Reference Angles

Find out which quadrant it is inIn the 1st quadrant, the reference angle is the SAME as the angle itselfIn the 2nd quadrant subtract the angle from 180o or πIn the 3rd

quadrant subtract 180

o

or

π from the angle

In the 4th quadrant subtract the angle from 360o or 2π

Slide23

Examples

Find the reference angle for the following angles. 37o7π/4-2π/3-190o17π/7

820

o

Slide24

PRACTICE