Sum and Difference Identities Part Two

Hi guys, it's mirajoy (: yesterday we learned more about sum and difference identities.

For example, when given a question like ...

"given that sinα= -8/7 and cosβ= 3/5 where α and β and in quadrants III and IV respectively, find the coordinates of P(α+β) and the quadrant in which the terminal side of P(α+β) lies."

• Remember when you are giving coordinates the x is cos and y is sin. so P(α+β) becomes P(α+β) = (cos(α+β) , sin(α+β))

-The first thing you have to do is find your α coordinates using soh cah toa and the Pythagorean theorem. Since sinα= -8/7 is found in quadrant III, draw your triangle in the third quadrant. Next, using soh cah toa label your opposite and hypotenuse. Then use the Pythagorean theorem to find the adjacent. then use soh cah toa again to find tanα and cosα. Then do the same thing to find your β using cosβ= 3/5.

-Once you find all α and β go back to P(α+β) = (cos(α+β) , sin(α+β)) to solve.

-Note that cos(α+β)=cosαcosβ - sinαsinβ and sin(α+β)= sinαcosβ + cosαsinβ

- Lastly, plug in the α and β values then solve using the same steps as last class' lesson. (: