Question

If the sine of an acute angle is 3/5, what is the cosine of
that angle?

Answer 1

The cosine of the angle is 4/5.

Explanation:

An acute angle is between 0º and 90º, in the first quadrant of the trigonometric circle, in which both the sine and the cosine are positive values.

For each angle
`\alpha`, we have that:

`\sin^(2){\alpha} + \cos^(2){\alpha} = 1`

We have that:

`sin(\alpha) = (3)/(5)`

So

`\sin^(2){\alpha} + \cos^(2){\alpha} = 1`

`((3)/(5))^(2) + \cos^(2){\alpha} = 1`

`\cos^(2){\alpha} = (16)/(25)`

`cos(\alpha) = (4)/(5)`

The cosine of the angle is 4/5.