1. 5.4 Sum and Difference Identities

2. Bell Ringer

3. 5.4 Sum and Difference Identities
Yesterday we took a look at basic trigonometric identities and we verified trigonometric identities.
Today we will use the sum and difference identities for the sine, cosine, and tangent functions
Tomorrow we will use the double-angle and half-angle identities for the sine, cosine, and tangent functions

4. back… To lesson 7.2 when you learned the distance formula
to lesson 4.7 when we were introduced to the Law of Cosines.

5. First use Law of Cosines

6. Now use the Distance Formula

7. Finally…
Set the two answers equal to each other

8. Sum & Difference Identities

9. Remember this???
It is very important
that you know
these values.

10. Simplify the expression. Find the exact value if possible
sin 20° cos 40° + cos 20° sin 40°

11. Simplify the expression. Find the exact value if possible.
Your Turn
Simplify the expression.
Find the exact value if possible.

12. The sum and difference identities for the sine function.

13. The sum and difference identities for the sine function.
Your Turn

14. The sum and difference identities for the cosine function.

15. The sum and difference identities for the cosine function.
Your Turn

16. The sum and difference identities for the tangent function.

17. The sum and difference identities for the tangent function.
Your Turn

18. Making Connections
Broadcasting Have you ever had trouble tuning in your favorite radio station? Does the picture on your TV sometimes appear blurry? Sometimes these problems are caused by interference. Interference can result when two waves pass through the same space at the same time. Two kinds of interference are
Constructive interference, which occurs if the amplitude of the sum of the waves is greater than the amplitudes of the two component waves and
Destructive interference, which occurs if the amplitude of the sum is less than the amplitude of the component waves.

19. What type of interference results when a signal modeled by the equation is combined with a signal modeled by the equation

20. Solution: Add the two equations together and simplify.
The interference is destructive. The signals cancel each other completely.

21. Find the value of
From the Pythagorean Theorem

23. Your Turn
Find the value of

25. Solve a trigonometric equation.

26. Solve a trigonometric equation.
Your Turn

27. HOT Question .
Describe how you would convince a friend that

28. Derive the sum identity for the tangent function
In your group…

29. Wrap-up What are the sum and difference formulas for the
sine function?
What are the sum and difference formulas for the cosine function?
What are the sum and difference formulas for the tangent function?

30. 5.4 Practice