If `sin theta`? `=60/61` then find `cos theta` and `tan theta`.

Explanation

To solve the problem, we need to find the values of \( \cos \theta \) and \( \tan \theta \) given that \( \sin \theta = \frac{60}{61} \).

### Step-by-Step Solution:

1. **Find \( \cos \theta \)**:
We know the Pythagorean identity:
\[ \sin^2 \theta + \cos^2 \theta = 1 \]
We can rearrange this to find \( \cos^2 \theta \):
\[ \cos^2 \theta = 1 - \sin^2 \theta \]

2. **Calculate \( \sin^2 \theta \)**:
Given \( \sin \theta = \frac{60}{61} \):
\[ \sin^2 \theta = \left(\frac{60}{61}\right)^2 = \frac{3600}{3721} \]

3. **Substitute \( \sin^2 \theta \) into the equation**:
Now substitute \( \sin^2 \theta \) into the equation for \( \cos^2 \theta \):
\[ \cos^2 \theta = 1 - \frac{3600}{3721} \]
To simplify, convert 1 into a fraction:
\[ 1 = \frac{3721}{3721} \]
Thus,
\[ \cos^2 \theta = \frac{3721 - 3600}{3721} = \frac{121}{3721} \]

4. **Take the square root to find \( \cos \theta \)**:
\[ \cos \theta = \sqrt{\frac{121}{3721}} = \frac{11}{61} \]

5. **Find \( \tan \theta \)**:
We know that:
\[ \tan \theta = \frac{\sin \theta}{\cos \theta} \]
Substitute the values of \( \sin \theta \) and \( \cos \theta \):
\[ \tan \theta = \frac{\frac{60}{61}}{\frac{11}{61}} = \frac{60}{11} \]

### Final Answers:
- \( \cos \theta = \frac{11}{61} \)
- \( \tan \theta = \frac{60}{11} \)