What is cosa if sina=2/7? a is an acute angle

Since a is an acute angle, that means that a<`pi/2`
, therefore we'll calculate the value of cosine function for an angle located within the
1st quadrant. In the 1st quadrant, all the values of trigonometric functions are
positive.

We'll use Pythagorean identity to compute cos
a:

`cos^2 a = 1 - sin^2
a`

`cos a = +sqrt(1 - sin^2
a)`

cos a = `+sqrt(1 -
4/49)`

cos a = `+sqrt
(45/49)`

cos a =
`+(3sqrt5)/7`

Therefore, the requested value of cosine of
the acute angle a is:

cos a = `+(3sqrt5)/7`
.