Section 13.2
Angles and the Unit Circle
Standard Position Angle (of 60°)
An angle is in standard
position when:
1) The vertex is at the
origin.
2) One leg is on the
positive x – axis.
(This is the initial side.)
3)
The second ray moves
in the direction of the
angle
(This is the terminal side.)
Reading Angles
If the movement from the
initial side to the terminal
side of the angle is
counterclockwise, then
the angle measures
positive.
+135°
Reading Angles
If the movement from the
initial side to the terminal
side of the angle is
clockwise, then the angle
– 225°
measures negative.
Measuring Angles
2)
1)
–315°
3)
240°
–110°
Coterminal Angles
Two angles in standard
position that have the same
terminal side are coterminal
Find the measure of an angle
between 0 ° and 360 °
coterminal with each given angle:
4)
575°
angles.
To find a coterminal angle
215 °
5)
4°
between 0 ° and 360 ° either
add or subtract 360 ° until you
get the number that you want.
–356°
6)
–210°
150 °
7)
–180°
180 °
The Unit Circle
1
The Unit Circle:
1
1)
Is centered at the origin,
2)
Has a radius of 1,
3)
Has points that relate to
periodic functions.
Normally, the angle measurement
is referred to as θ (theta).
Finding Values on the Unit Circle





For all values using
SOH, CAH, TOA the H
value is always 1.
We can use the
Pythagorean Theorem to
find the rest.
cos θ is the x coordinate.
sin θ is the y coordinate.
Let’s find sin (60°) and
cos (60°).
√3
2
1
½

On a 30-60-90 triangle the
short side is ½ the hypotenuse.

So, cos (60°) = ½.

a2 + b2 = c 2
(½)2 + b2 = 12

¼ + b2 = 1
b2 = ¾
b = √(¾) = √(3)/2
So, sin (60°) = √(3)/2
Finding Values on the Unit Circle

Continue to find the
values on the Unit Circle

Find cos 0° and sin 0°
(0, 1) 1
(½, √3/2)
(√2/2, √2/2)

Find cos 30° and sin 30°

Find cos 45° and sin 45°
(√3/2, ½)
(1, 0)
1

Find cos 90° and sin 90°
All Four Quadrants

These patterns repeat for the right x and y
values.

The values can be either positive or negative
based on the x and y axes.

Use this information to fill in the worksheets
with exact values
Finding Values
Locate the Unit Circle diagram from before.
8)
9)
10) –390°
11) –30°
sin (–60°) = –√(3)/2
cos (–60°) = ½
sin (–60°) = –½
cos (–60°) = √(3)/2
Extra Practice
 During
this lesson we completed page 708
# 1 – 27 odd.
 For
more practice, complete the even
problems