Precalculus Functions & Graphs 5.1 Angles Initial Side Terminal Side Math Illustrations Link We say an angle is in whatever Quadrant the terminal side.

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Presentation transcript:

Precalculus Functions & Graphs 5.1 Angles Initial Side Terminal Side Math Illustrations Link We say an angle is in whatever Quadrant the terminal side is in. If the terminal side moves counter-clockwise it is a positive angle if it moves clockwise it is negative.

Precalculus Functions & Graphs 5.1 Angles Coterminal Angles are angles with the same initial and coterminal sides. Math Illustrations Link Positive coterminal angles are found by adding multiples of 360 to the angle. Negative coterminal angles are found by subtracting multiples of 360 to the angle.

Precalculus Functions & Graphs 5.1 Angles Find two positive and two negative coterminal angles for each angle. Math Illustrations Link Example #1 Positive: add 360 to 135 and 360 to the sum of 360 and 135 Positive: subtract 360 from 135 and 360 from the difference of 360 and 135

Precalculus Functions & Graphs 5.1 Angles Find two positive and two negative coterminal angles for each angle. You Try #1 Notice 180 is not negative so we need to subtract 360 again.

Precalculus Functions & Graphs 5.1 Angles acute obtuse right straight complementary supplementary

Precalculus Functions & Graphs 5.1 Angles Find the complement and supplement for each angle given. Example #2 To find the complement subtract 55 from 90. To find the supplement subtract 55 from 180.

Precalculus Functions & Graphs 5.1 Angles Find the complement and supplement for each angle given. You Try #2 To find the complement subtract 27 from 90. To find the supplement subtract 27 from 180.

Precalculus Functions & Graphs 5.1 Angles Degree Minute Second 1 Degree 1 Minute 60 minutes 60 seconds

Precalculus Functions & Graphs 5.1 Angles Find the complement and supplement for each angle given. Example #3 To subtract we need to borrow a degree. Use the same process for 180. Now we need to borrow a minute.

Precalculus Functions & Graphs 5.1 Angles Find the complement and supplement for each angle given. You Try #3

Precalculus Functions & Graphs 5.1 Angles One radian is the measure of the central angle subtended by an arc equal in length to the radius of a circle. Math Illustrations Link What is the arc length of the unit circle? 6.28 Remember from Geometry that the formula for arc length is

Precalculus Functions & Graphs 5.1 Angles Math Illustrations Link

Precalculus Functions & Graphs 5.1 Angles To convertMultiply ByExample Degrees to radians Radians to degrees

Precalculus Functions & Graphs 5.1 Angles Convert from degrees to radians You Try #4 Convert from radians to degrees

Precalculus Functions & Graphs 5.1 Angles Example #4 First convert to degrees. To convert.8873 to minutes To convert.238 to seconds

Precalculus Functions & Graphs 5.1 Angles You Try #5 First convert to degrees. To convert.5494 to minutes To convert.964 to seconds

Precalculus Functions & Graphs 5.1 Angles Example #5

Precalculus Functions & Graphs 5.1 Angles

Precalculus Functions & Graphs 5.1 Angles Find the length of the arc in the sector of the figure, then find the area of the sector. Example #6 Convert 135 to radians

Precalculus Functions & Graphs 5.1 Angles You Try #6

Precalculus Functions & Graphs 5.1 Angles You Try #6