If `theta = -1440^(@)`, then `tan theta` is

Options

A. 1
B. 0
C. `-1`
D. `sqrt(3)`

Answer

To find \( \tan \theta \) when \( \theta = -1440^\circ \), we can follow these steps:

### Step 1: Find the equivalent positive angle
To convert \( -1440^\circ \) to a positive angle, we can add \( 360^\circ \) repeatedly until we get a positive angle.

\[ -1440 + 360 \times n = \text{positive angle} \]

We can divide \( 1440 \) by \( 360 \) to find how many full rotations fit into it:

\[ 1440 \div 360 = 4 \]

So, we can add \( 360^\circ \) four times:

\[ -1440 + 360 \times 4 = -1440 + 1440 = 0^\circ \]

### Step 2: Determine the value of \( \tan \theta \)
Now that we have \( \theta = 0^\circ \), we can find \( \tan 0^\circ \):

\[ \tan 0^\circ = 0 \]

### Step 3: Conclusion
Thus, we have:

\[ \tan(-1440^\circ) = \tan(0^\circ) = 0 \]

### Final Answer
\[ \tan(-1440^\circ) = 0 \]

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