Download Trigonometry Notes 1.1 Angles Day 2

Trigonometry
Notes 1.1 Angles Day 2
Learning Targets
I will learn Standard position and Coterminal angles.
1. Going in a counterclockwise rotation show a positive angle by starting at the initial side and
drawing an arrow to the terminal side.
2. Going in a clockwise rotation show a negative angle by starting at the initial side and drawing
an arrow to the terminal side.
Drawing an angle in standard position
1) Vertex is at the origin
2) Draw the initial side on the positive x-axis
3) Rotate the terminal side the amount of degrees given
a. Positive angles rotate counterclockwise
b. Negative angles rotate clockwise
Examples 1: Sketch the angles in standard position.
a) 168°
b) -80°
c) 545°
Example 2
An angle is in standard position if its vertex is at the origin and its initial side lies on the positive
x-axis. Draw the 4 angles below in 4 different quadrants. Show the initial side, the terminal
side, and the positive angle. An angle is said to lie in the quadrant in which its terminal side lies.
I
II
50 
120 
III
IV
210 
300 
Quadrantal Angles:
Angles in standard position whose terminal sides lie on the x or y axis. The angle measures are
0, 90, 180, 270, 360 degrees.
Draw each:
0  or 360 
90 
180 
270 
Angle A is 45 degrees. We will abbreviate this A  45
Coterminal Angles
Coterminal angles- angles that have the same initial side and terminal side, but different
amount of rotation. Their measures differ by a multiple of 360 degrees. n  360 
Example: 30 
3. Find the angle of least possible positive measure coterminal with each angle.
a) 30°
b) -450°
c) 1080°
4. Give 2 positive and 2 negative angles that are coterminal to
a) 10°
b) -90°
5. Give an expression that generates all angles coterminal with 45 . Let n represent any
integer.
6. Sketch the angle  150  in standard position. Draw an arrow representing the correct
amount of rotation. Find 2 other angles that are coterminal with  150  . Name the quadrant
 150  is in.