If `sin x = 3/(5)`, then cos x is

Options

A. `4/(5)` but not `-4/(5)`
B. `4/(5)` or `-4/(5)`
C. `-4/(5)` but not `4/(5)`
D. none of these

Answer

To find the value of \( \cos x \) given that \( \sin x = \frac{3}{5} \), we can use the Pythagorean identity:

\[ \sin^2 x + \cos^2 x = 1 \]

### Step-by-Step Solution:

1. **Start with the Pythagorean Identity**:
\[ \sin^2 x + \cos^2 x = 1 \]

2. **Substitute the value of \( \sin x \)**:
Since \( \sin x = \frac{3}{5} \), we find \( \sin^2 x \):
\[ \sin^2 x = \left(\frac{3}{5}\right)^2 = \frac{9}{25} \]

3. **Substitute \( \sin^2 x \) into the identity**:
\[ \frac{9}{25} + \cos^2 x = 1 \]

4. **Isolate \( \cos^2 x \)**:
\[ \cos^2 x = 1 - \frac{9}{25} \]

5. **Convert 1 to a fraction with a denominator of 25**:
\[ 1 = \frac{25}{25} \]
So,
\[ \cos^2 x = \frac{25}{25} - \frac{9}{25} = \frac{16}{25} \]

6. **Take the square root to find \( \cos x \)**:
\[ \cos x = \sqrt{\frac{16}{25}} = \frac{4}{5} \]

7. **Consider the sign of \( \cos x \)**:
Since we are not given the quadrant in which \( x \) lies, we typically take the positive root unless specified otherwise. Thus,
\[ \cos x = \frac{4}{5} \]

### Final Answer:
\[ \cos x = \frac{4}{5} \]