If the cosine of an angle is 7/25, what is the sine of that angle?

To find the sine of an angle when the cosine is given, you can use the fundamental trigonometric identity:

[

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

]

Since the cosine of the angle is provided as ( \frac{7}{25} ), you can calculate the sine using the following steps:

1. Substitute the known cosine value into the equation:

[

\sin^2(\theta) + \left(\frac{7}{25}\right)^2 = 1

]

2. Compute ( \left(\frac{7}{25}\right)^2 ):

[

\sin^2(\theta) + \frac{49}{625} = 1

]

3. Rearrange the equation to solve for ( \sin^2(\theta) ):

[

\sin^2(\theta) = 1 - \frac{49}{625}

]

[

\sin^2(\theta) = \frac{625}{625} - \frac{49}{625} = \frac{576}{625}

]

4. Take the square root to find ( \sin(\theta) ):

[

\