1. Angles in standard Position
Today we will draw angles in standard position and determine angles that are co-terminal.

2. B.y.o.d Warm-up Get out a piece of paper for today’s notes.
Please title the notes: “Angles in Standard Position”
Using your electronic device, please answer the following questions? Draw any graphs that support your explanations.
What is an angle?
What does it mean for an angle to be in standard position?
What is an initial ray and a terminal ray?

3. What is an angle?
It is composed of 2 rays:

4. Standard position
An angle is in standard position if its vertex is located at the origin and one ray is on the positive x-axis (called the initial ray).
Important note:
Positive angles rotate counterclockwise
Negative angles rotate clockwise

5. Examples of angles in standard position

6. Which helps us establish this graph
Quadrantal angles
These angles terminate on an axis:
Example:
Which helps us establish this graph
,360º

7. You try.
Draw the following angles in standard position:
45º
225º
-540º

8. Co-terminal angles
Angles that share the same initial side and terminal sides.
To generate co- terminal angles, it is as simple as adding or subtracting 360º

9. You try Give three angles that are co-terminal with 150º.
Sample answers: -210º; 510º, 870º

10. Next up
Discovering Radians Activity

11. Radians
As established in the “Discovering Radians Activity,” 2π = 360º. Use this information to convert the following degree measurements to radians:
90º
180º
270º

12. This leads to….
360º, 2π

13. Establishing radian measurement
3π/4
π/4
Convert 45ºdegree to radians and then place on your circle:
Which then helps you establish radians in other quadrants
360º, 2π
5π/4
7π/4

14. You try. Convert 60ºdegree to radians and then place on your circle.
π/3
2π/3
Convert 60ºdegree to radians and then place on your circle.
Now place the other measurements in the remaining quadrants.
360º, 2π
4π/3
5π/3

15. You try. Convert 30ºdegree to radians and then place on your circle.
Now place the other measurements in the remaining quadrants.
5π/6
π/6
360º, 2π
7π/6
11π/6

16. Exit Ticket---Now, use all of the info to sketch the following angles in standard position.
11π/6
5π/4
-π/2 4π
-2π/3
5π/2
Homework: p. 105: 11-22