Given that sinA = 2/3 and A is acute find cos(A) \sin(a) = (2)/(3)

Question

Given that sinA = 2/3 and A is acute find cos(A)

`\sin(a) = (2)/(3)`

Answer 1

Recall that

`\sin^2a+\cos^2a=1\implies\cos^2a=1-\frac49=\frac59`

`\implies\cos a=\pm\frac{\sqrt5}3`

Angle
`a` is acute, which means its measure is between 0 and 90 degrees. For
`0^\circ<a^\circ<90^\circ`, we have
`\cos a>0`, so we should take the positive root. Then

`\cos a=\frac{\sqrt5}3`