1. 7.2.1 – Sum and Difference Identities

2. A new set of identities we will deal with will allow us to determine exact trig values of angles on the unit circle that we do not know – Example: sin(35 0 )?

3. Motivation allows us to avoid calculator use, and be more precise when talking of applied terms – Engineering: Must know exact angles to measure – Anatomy: Exact values when talking of angles of flexion or similar

4. Sum and Diff: Sine Let u and v be two unique angles sin(u + v) = sin(u)cos(v) + sin(v)cos(u) sin(u – v) = sin(u)cos(v) – sin(v)cos(u)

5. Sum and Diff: Cos Let u and v be two unique angles cos(u + v) = cos(u)cos(v) - sin(v)sin(u) cos(u – v) = cos(u)cos(v) + sin(v)sin(u)

6. Sum and Diff: Tan Let u and v be two unique angles:

7. Using these, we can determine angles in two ways: 1) Use literally in the sense of u + v 2) Write an angle as the sum of two known angles from the unit circle (30, 45, 60, 90,…) Always make sure to use angles whose sin, cos, or tan values can be readily referenced (go back to our chart)

8. Example. Determine the value of Cos( )

9. Example. Determine the value of sin( )

10. Example. Determine the exact value of tan( )

11. If we need to find the value of an angle, say for 195 0, we must determine what sum, or difference, of two angles we can reference from the unit circle that we may use

12. Example. Determine the exact value of cos(195 0 )

13. Example. Determine the exact value of cos( )

14. Assignment Pg. 564 1, 2, 4, 13, 15, 21, 24, 27, 39