I chose this topic because it is the first lesson of the trigonometry unit.

 

Identifying Rotation Angles less than 360°

 

To identify rotation angles, the measure of the amount that the line is rotated after a fixed point, we must understand the angle in each “arm” of the x-y axis. See illustration below for the angles. We also need to understand where the quadrants are.

• Step 1: Find the line. To find the line, first find the point on the axis. The point will be connected to the vertex to create a line.
• Step 2: Follow the formula & Evaluate. Depending on the quadrant it is in, finding the rotation angle requires the following formula:

QI (top right): rotation angle=angle

QII (top left): 180°-angle= rotation angle

QIII (bottom left): 180°+angle= rotation angle

QIV (bottom left): 360°-angle= rotation angle

 

example 1:

point: (5,10)

rotation angle:

QI (top right): 65°= 65°

 

example 2:

 

point: (-4, -8)

rotation angle:

QIII (bottom left): 180°+65°= 245°