1. Sum and Differences Of Periodic Functions
Dr. Shildneck
Spring, 2015

2. Derive the Cosine of a Difference
Using the Unit Circle to
Derive the Cosine of a Difference

3. Given two angles, u and v, we want to find a formula for the cosine of the difference between u and v. v
θ = u - v u

4. θ

5. for the lengths of the two segments.θ
θ = u - v
Since , we can write an equivalence relation using the distance formula
for the lengths of the two segments.

6. Derive the Cosine of a Sum
Now…
we can use the previous identity and the even/odd identities to
Derive the Cosine of a Sum
And…

7. Derive the Sine of a Sum and The Sine of a Difference
Then…
we can use the previous identities, co-function identities, and even/odd identities to
Derive the Sine of a Sum and The Sine of a Difference
And…

8. Derive the Tangent of a Sum and The Tangent of a Difference
And then…
we can use the previous identities, quotient identities, and even/odd identities to
Derive the Tangent of a Sum and The Tangent of a Difference
But… we aren’t going to… So, here are the rest…

9. SUM and DIFFERENCE IDENTITIES
sin(1st)cos(2nd) [same operation] sin(2nd)cos(1st)
cos(1st)cos(2nd) [opposite operation] sin(1st)sin(2nd)

10. Example 1
Find the exact value of
C) Find the exact value of

11. Example 2
Find the exact value of

12. Example 3
Simplify the expression:

13. Example 4
Simplify the expression:

14. Example 5
Write as an expression of x.

15. Example 6 Find the exact value of if ,
in Quadrant 1 and in Quadrant 2.

16. ASSIGNMENT
Assignment 2 WS