In a right triangle, if the sine of angle A is three-fifths, what is the cosine of angle A?

To determine the cosine of angle A in a right triangle when the sine of angle A is three-fifths, we can use the Pythagorean identity which states that the square of the sine of an angle plus the square of the cosine of the same angle equals 1. This can be expressed mathematically as:

[

\sin^2(A) + \cos^2(A) = 1

]

Given that (\sin(A) = \frac{3}{5}), we can find (\sin^2(A)):

[

\sin^2(A) = \left(\frac{3}{5}\right)^2 = \frac{9}{25}

]

Now we plug this value into the identity:

[

\frac{9}{25} + \cos^2(A) = 1

]

To isolate (\cos^2(A)), we subtract (\frac{9}{25}) from both sides:

[

\cos^2(A) = 1 - \frac{9}{25} = \frac{25}{25} - \frac{9}{25} = \frac{16}{25}

]

Now, to find \