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.– 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 1/8th 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 360o.

Example:

• Find the coterminal angle, θ, for each angle below such that -360o<θ<360o. 180o

-27o

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.

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: 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

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