### 6.1. Angles of Rotation (Coterminal Angle, RAA).notebook

```6.1. Angles of Rotation (Coterminal Angle, RAA).notebook
May 28, 2014
Unit 6 ­ Trigonometry II
Lesson 1: Angles of Rotation
Grade 10: Solve sinθ = 0.866
Looking at the sine function, where θ is the angle and y is the trig ratio, we see that there are more possible answers since y = sinθ is periodic.
∴ θ =
are all solutions to the trig equation sinθ = 0.866 because we o
must take into account all angles < 0 and > 90.o
6.1. Angles of Rotation (Coterminal Angle, RAA).notebook
May 28, 2014
Angles of Rotation
We use the cartesian plane to account for angles greater than o
90 .
Counter clockwise rotation shows a positive angle.
Clockwise rotation shows a negative angle.
The rotation is indicated by a directed arrow starting at the positive x­axis (θ is in standard position).
Ex.1. State the angle of rotation.
(b)
a)
60
o
60
(c)
o
o
45
Two angles in standard position are coterminal if they have the same terminal arm. Coterminal angles differ by a multiple o
of 360.
∴ Examples a & b above are coterminal.
6.1. Angles of Rotation (Coterminal Angle, RAA).notebook
May 28, 2014
o
Ex.2. Find three angles coterminal with 80 .
Ex.3. For angles α and θ, determine if they are coterminal
o
o
a) α = 57 θ = 1137
o
(b) α = 340 θ = ­400
o
6.1. Angles of Rotation (Coterminal Angle, RAA).notebook
May 28, 2014
Angles of any measure have a Related Acute Angle (β) associated with them. The RAA (β) is the acute (less than 90 ) angle (can be shown in a ) that is formed between the terminal arm and the x­axis.
We always draw a line up/down to the x­axis. This
drawn is very useful in trigonometry
Ex.4. Find the RAA, β, for each angle θ. Draw the line with the x­axis.