JMerrill, 2009

An angle is said to be in standard position if its initial side is along the positive x -axis and its vertex is at the origin.
We say that an angle lies in the quadrant in which its terminal side lies.

180 o
Quadrant II
Quadrant III
90 o
Quadrant I
Quadrant IV
0 o
360 o
270 o

Sketching a 210 º angle in the standard position yields this graph.
• The initial side lies on the x -axis.
• The positive angle indicates counterclockwise rotation.
• 180 º represents a straight angle and the additional 30º yields a
210 º angle.
• The terminal side lies in quadrant III.
• What can you tell me about the angle -150 o ?

Two angles in standard position with the same terminal side are called coterminal angles . For example, -40 º and
320º are coterminal angles. Moving 40º in clockwise direction brings the terminal side to the same position as moving 320º in the counter-clockwise direction.
Such angles may also be reached by going the same direction, such as 90 º and 450º. 450º is reached by moving counterclockwise through the full 360º circle, then continuing another 90 º.
So, you can find coterminal angles by adding or subtracting a whole circle.

Your Turn:
Measuring of Coterminal Angles
Find an angle that is coterminal with:
 580 º
 Solution: Subtract 360º to find the correct angle of 220º.
 400º
 Solution: Add 360º to get -40º. Add 360º again to get the correct angle of 320º.

The common angles with their exact values for their Cartesian coordinates are shown on this graph.