What is the value of `tan(405^(@))`

Options

A. `(1)/(2)`
B. `-sqrt3`
C. `-1`
D. 1

Answer

To find the value of \( \tan(405^\circ) \), we can follow these steps:

### Step 1: Reduce the angle
The tangent function has a periodicity of \( 180^\circ \). This means that \( \tan(\theta) = \tan(\theta + 180^\circ n) \) for any integer \( n \). We can reduce \( 405^\circ \) by subtracting \( 360^\circ \) (a full rotation):

\[ 405^\circ - 360^\circ = 45^\circ \]

### Step 2: Find the tangent of the reduced angle
Now, we need to find \( \tan(45^\circ) \). From trigonometric values, we know that:

\[ \tan(45^\circ) = 1 \]

### Step 3: Conclusion
Thus, the value of \( \tan(405^\circ) \) is:

\[ \tan(405^\circ) = \tan(45^\circ) = 1 \]

### Final Answer:
The value of \( \tan(405^\circ) \) is \( 1 \).

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