Question

Given: cos α = 4/5, sin β= 4/5, and α and β are both in quadrant 1. find sin (α+β)

Answer 1

We have the formula (sin x)^2 + (cos x)^2 = 1;
Then, sin α = $\sqrt{1- ( \frac{4}{5}) ^{2} } = \frac{3}{5} ;$
cos β = $\sqrt{1- ( \frac{4}{5}) ^{2} } = \frac{3}{5} ;$
We apply the formula sin ( α + β ) = sin α x cos β + sin β x cos α = (3/5)x(4/5) + (4/5)x(3/5) = 12/25 + 12/25 = 24/25;