1. The measure of an angle is a number that represents the size
and direction of rotation used to generate the angle.
In Trigonometry:
1. Angles generated by counterclockwise rotations are measured with POSITIVE
NUMBERS.
2. Clockwise rotations NEGATIVE NUMBERS
An angle is in STANDARD POSITION if its vertex is at the origin and its initial
side is the positive x­axis.

2. Remember
Q2 Q1
Q3 Q4

3. Coterminal Angles are angles in standard position having the same terminal side.
Note: There are two ways to arrive at the final angle.
o
100
The difference of the two angles
is 360o or a multiple of 360o
Look at sketchpad file "Terminal­Initial sides of rotations"

4. Examples
1.
2.
3. Find the angle of smallest positive measure coterminal with:
a) 4000
b) 7100

5. Sine, Cosine, and Tangent are defined in terms of the ratios of sides of
right triangles and limited to positive acute angles (because of the
triangles).
Notice <POD. The circle is called
The Unit Circle because it's radius is 1 unit.
P (x,y)
Find the values of x and y.
650 D (1,0)
O

6. Solution
P (x,y)
1
y
θ0 D (1,0)
O x
Therefore in a unit circle, given an angle of θ0, the coordinates of P are (cos θ, sin θ).

7. Find Tan θ
P (cosθ,sinθ)
650 D (1,0)
O
Note: When cos θ equals zero, which occurs
at any odd multiple of 900, then tanθ is UNDEFINED!

8. When are the values of trig functions positive or negative?
00< θ < 900
900< θ < 1800
1800< θ < 2700
2700< θ < 3600
P (x,y)
650 D (1,0)
O

9. Attachments
Terminal­Initial Sides of Rotations.gsp