1. Aim: How do we look at angles as rotation?
Do Now: Draw the following angles:
a) 60
b) 150
c) 225

2. An angle is formed by joining the endpoints of two half-lines called rays.
The side you measure to is called the terminal side.
Angles measured counterclockwise are given a positive sign and angles measured clockwise are given a negative sign.
Terminal Side
Positive Angle
This is a counterclockwise rotation.
Negative Angle
This is a clockwise rotation.
Initial Side
The side you measure from is called the initial side.

3.       It’s Greek To Me! The most used symbol is θ alpha beta
It is customary to use small letters in the Greek alphabet to symbolize angle measurement.   
alpha
beta
gamma   
theta
phi
delta
The most used symbol is θ

4. We can determine the quadrant an angle is in by where its terminal side is in a standard position.
Standard position: Vertex at (0,0) initial side is the positive x-axis.
Use four different angles in all four quadrants to show that
If then the angle is in Quadrant I
If then the angle is in Quadrant II
If then the angle is in Quadrant III
If then the angle is in Quadrant IV

5. Terminal sides Angles at each quadrant on standard position y
Initial side x
Terminal sides

6. What happen if an angle is on the axis?
We call the angle whose terminal side on either axis as quadrantal angles.
Quadrantal angle is the angle whose degree measure is multiple of 90.
For example etc.,
Example: Determine which quadrant is the angle in?
a) 145 b) 240 c) 292 d) 75

7. We call the angles that have the same terminal sides in a standard position as coterminal angles.
If two angles are coterminal, the difference in their measures is 360º or a multiple of 360º
For example: angle 80 is the same angle as
– 280
80 – (-280) = 360
Find the coterminal angle of 150
150 – x= 360, x = – 210

8. Determine the angles are coterminal or not:
1630, 910
5500, -170
1630, 50

9. Very simple: We just need to divide the angle by 360
If angle whose measure is greater than 360, how do we find the coterminal angle?
Very simple: We just need to divide the angle by 360
, the remainder is the degree measure of the coterminal angle.
For example: Find the smallest coterminal angle of
860that is less than 360 .
Remainder is 140
and remainder is 140therefore, the coterminal angle is 140or -220

10. Find the smallest coterminal angle less than 360
930
1080
210 0
Determine which quadrant the angles locate II
170
350
-165
460
-210 IV
III II II

11. Another unit to measure angle is the radian
Degree Vs Radian
To measure an angle we can another unit besides degree
Another unit to measure angle is the radian
Radian is the central angle that intercepts an arc whose length is the same as the radius.

12. O 
r = 1
1 radian
Arc length = 1
The circle has radius equals 1. The central of the circle that intercepts the arc with length 1 is equal to 1 radian
Use the same reason, if the radius is 2 units then the central angle equals 1 radian when the intercepted arc is also 2 units

13. One circle = 360° (degrees)
One circle = 2π radians
1π radians = 180°
90  /2 radians
270  3/2 radians

14. The rules for conversion of degree & radian
Degree to radian
Radian to degree
Convert 75 to radian in terms of  36
Convert to degree

15. Convert into degree 1.
18 2.
72 3.
135 4.
330

16. Convert into radian
1. 240
2. 200 
4. 500