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
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Slide1
Degrees and Radians
Slide2Initial side – start side of angle
Terminal side – end side of angleStandard position – An angle whose initial side is on the positive x-axis
Slide3Positive angles
An angle in standard position that rotates counterclockwise
Slide4Negative angles
An angle in standard position that rotates clockwise
Slide5Coterminal
AnglesAngles that have the same terminal side
Slide6Simplify the Angles:
http://www.mathopenref.com/trigangle.html
Slide7Quadrants
Quadrant III
Quadrant I
Quadrant II
Quadrant IV
Slide8Angles of the axes
What quadrant is it in (and sketch)?
Slide9Variables you will see for angle measures
Slide10Radian
: made by taking the radius and wrapping it along the arc (edge of the circle)
http://www.mathopenref.com/radians.html
Slide11Slide12Radians
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
Slide13Radians 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
Slide14Angles of the axes in radians
Examples – quadrant &
skecth
Slide15Conversion Examples
Change from degrees to radiansChange from radians to degrees
Slide16Coterminal
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
Slide17Examples for radians
Find a positive and negative coterminal angle
Slide18Complementary/Supplementary
Complementary angles add up to 90o (or π/2 for radians)
Supplementary angles add up to 180
o
(or
π
for radians)
Slide19Examples
What angle is complementary/supplementary to 36o ?What angle is complementary/supplementary to 110o ?
Slide20Examples - radians
What angle is complementary/supplementary to ?What angle is complementary/supplementary to ?
Slide21Reference Angles
A reference angle is the acute angle that an angle makes with the x-axis
Slide22Finding 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
Slide23Examples
Find the reference angle for the following angles. 37o7π/4-2π/3-190o17π/7
820
o
Slide24PRACTICE