Radians and Angles

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Radians and Angles
Welcome to Trigonometry!!
Starring
The Coterminal Angles Supp Comp Angles The
Converter
And introducing
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THE UNIT CIRCLE
You I are gonna be great friends!
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formed by rotating a ray about its endpoint
(vertex)
Ending position
Starting position
Initial side on positive x-axis and the vertex is
on the origin
Standard Position
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Angle describes the amount and direction of
rotation
Positive Angle- rotates counter-clockwise
(CCW) Negative Angle- rotates clockwise (CW)
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1 Radian measure of central angle, ?, that
intercepts the arc that has the same length as
the radius of the circle
Arc length s radius when ? 1 radian
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Calculate the number of radians in one full
circle
C
? 3.14
0, 2? 0, 6.28
0
Therefore, we can say that 1 full revolution 2?
radians.
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Coterminal Angles
Two angles with the same initial and terminal
sides
Find a positive coterminal angle to 20º
Find a negative coterminal angle to 20º
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What did you find?
These are just two possible answers.
Rememberthere are more! ?
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Complementary Angles Two angles whose sum is 90?
Supplementary Angles Two angles whose sum is
180?
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Convert to radians
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Convert to degrees
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1 degree 60 minutes 1 60 ?
1 minute 60 seconds 1 ? 60 ?
3600
So 1 degree _________seconds

Express 36?50?10?as decimal degrees
36
36
.8333
.00277
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OR
Express 36?50?10?as decimal degrees
Use your calculator!!
Enter 36
Press this button ?
Press enter
Enter 50
Press this button ?
Go over to the symbol -- enter
Enter 10
Press this button ?
Go over to the symbol -- enter
Press enter
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Convert 50? 47 50 to decimal degree
50.7972
Convert 125? 27 6 to decimal degree
125.4517
Can you go backwards and convert the decimal
degree to degrees minutes seconds?
Enter 125.4517 Go to DMS hit enter.
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Express 50.525? in degrees, minutes, seconds
50º .525(60) ?
50º 36.5?
50º 36? .5(60) ?
50 degrees, 36 minutes, 30 seconds
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