Given cossqrt558 and 2

Given cos()=sqrt(55)/8 and /2<< and cos()=sqrt(32)/9 and is in quadrant IV. Use sum and difference formulas to find the following:
Note: You are not allowed to use decimals in your answer.

sin(+)=

Solution

cos alpha= -sqrt55/8

here adjacent = sqrt 55 and hypotenuse=8

Therefore opposite= sqrt(64-55)=3

Sin alpha= 3/8

cos beta= sqrt 32/9

adjacent= sqrt 32 and hypotenuse=9

Therefore opposite= 7

sin beta=7/9

sin (alpha + beta)= sin alpha cos beta + cos alpha sin beta

                          = (3/8)(sqrt32/9)+ (-sqrt 55/8)(-7/9)

                          = (3sqrt32    + 7sqrt 55)/72