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13.2 Angles of Rotation
Unit Circle Quiz: May 11
Ch. 13 Test: May 13
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Do you recall…
• In geometry, an angle is defined by two rays that have a common endpoint.
• In trig, an angle is defined by a ray that is rotated around the endpoint…this is called ANGLE OF ROTATION.– The Greek letter theta, Θ, is commonly used to name
an angle of rotation.
• The starting position is the Initial Side and the final position is the TERMINAL SIDE.
• When the endpoint is at the origin, it is called STANDARD POSITION.
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What else?
• If rotated COUNTERCLOCKWISE- the angle has a positive measure
• If rotated CLOCKWISE-the angle has a negative measure
• The most common unit for angle measure is the degree.
• A complete rotation is 360 degrees, so 45 degrees is 1/8th of a complete rotation.– (hint…divide)
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COTERMINAL
• Two angles are co-terminal if they have the same terminal side.– What is co-terminal with 230 degrees?
• You can find the co-terminal angles by adding or subtracting integer multiples of 360o.
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Example:
• Find the coterminal angle, θ, for each angle below such that -360o<θ<360o. 180o
-27o
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Reference Angles
• For an angle in standard position, the reference angle, Θref , is the positive acute angle formed by the terminal side and the x-axis.
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Example:
• Find the reference angle for: 94 degrees
245 degrees
290 degrees
-110 degrees
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Trig Functions
• Let P(x,y) be a point on the terminal side in standard position. The distance from the origin to P is: 2 2x y
yr
x
0,tan
cos
sin
xx
yr
xr
y
0,cot
0,sec
0,csc
yy
x
xx
r
yy
r
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Example:
• Let P(-2,-3) by a point on the terminal side in standard position. Find the exact values of the 6 trig functions.
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Let’s make you think…
• The terminal side of Θ in standard form is in Quadrant II and cos Θ = -3/5. Find the exact values of the 6 trig functions.
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Practicing Helps You Remember
• P. 841 #9 – 63 odd