1. Finding Reference Angles

2. It is necessary to be able to make larger angles smaller
It is necessary to be able to make larger angles smaller. We do this by finding reference angles:
Step:
Start by drawing the given angle
Now, we determine how many degrees it is until we get to the x-axis (horizon)
This is your reference angle
A reference angle is always positive
Determine the reference angle for 140 degree angle.
40 degrees is the reference angle for 140 degrees
A reference angle must be an ACUTE angle!!

3. Determine the reference angle for a 240 degree angle.
In the first quadrant, the angles are acute, so no need to find a reference angle.

4. Determine the reference angle for a 470 degree angle.

5. Homework
Page 8 & 9
#16,28

6. Applications of reference angles:
Express as a function of a positive acute angle:
Step:
Start by drawing the given angle
Find the reference angle
Rewrite the function using reference angle
Determine SIGN of function in quadrant where it was drawn
What is tan in quadrant II? S A T C

7. Express as a function of a positive acute angle:

8. Applications of reference angles: Step:
Start by drawing the given angle
Find the reference angle
Rewrite the function using reference angle
Determine SIGN of function in quadrant where it was drawn
Now find exact value using exact value chart
Find the exact value of each expression:
Reference angle
Since cos is negative in quadrant II, then the exact value is negative as well
Cos in quad II is negative

9. Find the exact value of each expression:

10. Find the exact value of each expression:

11. Find the exact value of each expression:

12. Exact Values of quadrantal angles:
We are going to graph four points and use our knowledge of the unit circle to help us!
y-value is sin
Just use these points to find the sin or cos of any angle falling on that line.

13. Exact Values of quadrantal angles:
Remember:
How do we find tan of these angles?
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14. Homework
Page 8 & 9
#8-14,21,24