Question

cosseno de a= 3/5 seno de B= 1/3 cacula seno de (a+b)

Answer 1

sen²a + cos²a = 1
sen²a + (3/5)² = 1
sen²a = 25/25 - 9/25
sen²a = 16/25
sen a = √(16/25)
sen a = 4/5

cos²b = 1 - sen²b
cos²b = 1 - (1/3)²
cos²b = 1 - 1/9
cos²b = 9/9 - 1/9
cos²b = 8/9
cos b = √8/9
cos b = 2√2/3

sen (a+b) = sen a cos b + sen b cos a
sen (a+b) = 4/5 . 2√2/3 + 1/3 . 3/5
sen (a+b) = 8√2/15 + 1/5
sen (a+b) = 8√2/15 + 3/15
sen (a+b) = (8√2+3)/15