Which of the following is not CORRECT ??

Options

A. ` sintheta = (-1)//(5)`
B. `costheta = 1`
C. ` sectheta =( 1)/(2)`
D. ` tantheta = 20`

Answer

To determine which of the given options is not correct, we will analyze each option based on the properties and ranges of the trigonometric functions involved.

### Step-by-Step Solution:

1. **Analyze Option 1:**
- Option 1 states: \( \sin \theta = -\frac{1}{\pi} \).
- The range of \( \sin \theta \) is from -1 to 1.
- Since \( -\frac{1}{\pi} \) is approximately -0.318, which lies within the range of \( \sin \theta \), this option is **correct**.

**Hint:** Remember that the sine function has a range of values between -1 and 1.

2. **Analyze Option 2:**
- Option 2 states: \( \cos \theta = 1 \).
- The range of \( \cos \theta \) is also from -1 to 1.
- Since 1 is within this range, this option is **correct**.

**Hint:** The cosine function can take values from -1 to 1, including the endpoints.

3. **Analyze Option 3:**
- Option 3 states: \( \sec \theta = \frac{1}{2} \).
- Recall that \( \sec \theta = \frac{1}{\cos \theta} \).
- If \( \sec \theta = \frac{1}{2} \), then \( \cos \theta = 2 \).
- However, the range of \( \cos \theta \) is from -1 to 1, and 2 is outside this range. Therefore, this option is **incorrect**.

**Hint:** The secant function is the reciprocal of the cosine function, and the cosine function cannot exceed 1 or be less than -1.

4. **Analyze Option 4:**
- Option 4 states: \( \tan \theta = 20 \).
- The range of \( \tan \theta \) is from \(-\infty\) to \(\infty\).
- Since 20 is within this range, this option is **correct**.

**Hint:** The tangent function can take any real number value, including large positive numbers.

### Conclusion:
After analyzing all the options, we find that:
- Option 1 is correct.
- Option 2 is correct.
- Option 3 is incorrect.
- Option 4 is correct.

Thus, the option that is **not correct** is **Option 3**: \( \sec \theta = \frac{1}{2} \).