13.2 Angles of Rotation Unit Circle Quiz: May 11 Ch. 13 Test: May 13

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. –T–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.

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 1/8 th of a complete rotation. –(hint…divide)

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 360 o.

Example: Find the coterminal angle, θ, for each angle below such that -360 o <θ<360 o.  180 o  -27 o

Reference Angles For an angle in standard position, the reference angle, Θ ref, is the positive acute angle formed by the terminal side and the x-axis.

Example: Find the reference angle for:  94 degrees  245 degrees  290 degrees  -110 degrees

Trig Functions Let P(x,y) be a point on the terminal side in standard position. The distance from the origin to P is: y r x

Example: Let P(-2,-3) by a point on the terminal side in standard position. Find the exact values of the 6 trig functions.

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.

Practicing Helps You Remember P. 841 #9 – 63 odd