If `tan45^(@)=cottheta` , then the value of `theta` , in radians is

Options

A. `pi`
B. `(pi)/(9)`
C. `(pi)/(4)`
D. `(pi)/(12)`

Answer

To solve the equation \( \tan 45^\circ = \cot \theta \) and find the value of \( \theta \) in radians, we can follow these steps:

### Step 1: Understand the given equation
We start with the equation:
\[ \tan 45^\circ = \cot \theta \]
We know that \( \tan 45^\circ \) is a standard angle in trigonometry.

**Hint:** Recall the value of \( \tan \) for common angles.

### Step 2: Calculate \( \tan 45^\circ \)
The value of \( \tan 45^\circ \) is:
\[ \tan 45^\circ = 1 \]
So we can rewrite the equation as:
\[ 1 = \cot \theta \]

**Hint:** Remember that \( \cot \theta \) is the reciprocal of \( \tan \theta \).

### Step 3: Relate \( \cot \theta \) to \( \tan \theta \)
Since \( \cot \theta = 1 \), we can express this in terms of \( \tan \):
\[ \cot \theta = \frac{1}{\tan \theta} \]
Thus, if \( \cot \theta = 1 \), then:
\[ \tan \theta = 1 \]

**Hint:** Think about what angle has a tangent value of 1.

### Step 4: Find the angle \( \theta \)
The angle \( \theta \) for which \( \tan \theta = 1 \) is:
\[ \theta = 45^\circ \]

**Hint:** Remember to convert degrees to radians.

### Step 5: Convert \( \theta \) to radians
To convert \( 45^\circ \) to radians, we use the conversion factor:
\[ \text{radians} = \frac{\pi}{180} \times \text{degrees} \]
So,
\[ \theta = 45^\circ = \frac{\pi}{180} \times 45 = \frac{\pi}{4} \]

**Hint:** Simplify the fraction to find the final value in radians.

### Final Answer
Thus, the value of \( \theta \) in radians is:
\[ \theta = \frac{\pi}{4} \]