1. Discovering sum & Difference identities
© Teresa Scar Fuston 2019

2. Use the unit circle to find the following: sin(60°) = sin(150°)= sin(210°)= sin(60°+150°)= sin(60°) + sin(150°)= Is sin(60°+150°) = sin(60°) + sin(150°) ?
NO!
© Teresa Scar Fuston 2019

3. So ... If sin(a + b) ≠ sin(a) + sin(b), what is ... sin(a + b) = cos(a + b) = We are so glad you asked! :)
© Teresa Scar Fuston 2019

4. In a right triangle, so so Label the legs in the right triangle.
© Teresa Scar Fuston 2019

5. Label the sides of the shaded triangle like we did on the previous slide … notice the angle is now . 1  
© Teresa Scar Fuston 2019

6. That allows us to label the other angle.
Since we have parallel lines cut by a transversal, alternate interior angles are congruent.
+ 1
That allows us to label the other angle.  
© Teresa Scar Fuston 2019

7. Now label the sides of this shaded triangle using the angle (+).1  
© Teresa Scar Fuston 2019

8. The next shaded triangle is different because the hypotenuse is not 1
The next shaded triangle is different because the hypotenuse is not 1! A few slides ago we saw that and Label the sides of this triangle.   1
+
© Teresa Scar Fuston 2019

9. We can find the marked angle using geometry and algebra.
+ 1  
© Teresa Scar Fuston 2019

10. Label the sides of the last triangle!
+ 1  
© Teresa Scar Fuston 2019

11. Compare the vertical sides of the rectangle. They’d have equal lengths
Compare the vertical sides of the rectangle. They’d have equal lengths. So …
+ 1  
© Teresa Scar Fuston 2019

12. Compare the horizontal sides of he rectangle. They’d have equal lengths. So … and, with algebra …
+ 1  
© Teresa Scar Fuston 2019

13. So ... If sin(a + b) ≠ sin(a) + sin(b), sin(a + b) = sinacosb + cosa sinb cos(a + b) = cosa cosb  sina sinb Ta-Da! :)
© Teresa Scar Fuston 2019