Which of the following is the least? sin 3 (b) sin 2 (c) sin 1 (d) sin 7

Options

A. sin 3
B. sin 2
C. sin 1
D. sin 7

Explanation

To determine which of the following values is the least among \( \sin 3 \), \( \sin 2 \), \( \sin 1 \), and \( \sin 7 \), we can analyze the sine function and its values at these specific angles.

### Step-by-Step Solution:

1. **Understanding the Sine Function**:
The sine function, \( \sin x \), oscillates between -1 and 1 for all real numbers \( x \). The function is periodic with a period of \( 2\pi \).

2. **Calculate Each Value**:
We will calculate \( \sin 3 \), \( \sin 2 \), \( \sin 1 \), and \( \sin 7 \) using a calculator or sine tables.

- \( \sin 1 \) (in radians) is approximately \( 0.8415 \).
- \( \sin 2 \) (in radians) is approximately \( 0.9093 \).
- \( \sin 3 \) (in radians) is approximately \( 0.1411 \).
- \( \sin 7 \) (in radians) is approximately \( 0.6569 \).

3. **Comparison of Values**:
Now we compare the calculated values:
- \( \sin 1 \approx 0.8415 \)
- \( \sin 2 \approx 0.9093 \)
- \( \sin 3 \approx 0.1411 \)
- \( \sin 7 \approx 0.6569 \)

4. **Identify the Least Value**:
From the values calculated:
- \( \sin 3 \) is the smallest value among the four.

5. **Conclusion**:
Therefore, the least value is \( \sin 3 \).

### Answer:
The least value is \( \sin 3 \) (Option a).