If sin alpha 35 and sin beta 1213 alpha and beta are in Qu

If sin alpha = 3/5 and sin beta = 12/13 alpha and beta are in Quadrant 1. Draw a diagram to assist you a. Find cos (alpha) exactly b. Find tan (beta) exactly c. Find sin (alpha + beta) exactly

Solution

sin alpha=3/5

cos alpha=sqrt(25-9)/5 = 4/5

sin beta=12/13

cos beta=sqrt(169-144)/13 =5/13

tan beta=sin beta/cos beta =12/5

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

=(3/5)(5/13)+(4/5)(12/13) =63/75=21/25