QuestionFind the value of $\tan 720^{\circ}$ or state if it is undefined.

Studdy Solution

STEP 1

Assumptions1. We are asked to find the value of $\tan720^{\circ}$ . . We know that the tangent function has a period of $180^{\circ}$ , which means $\tan \theta = \tan (\theta + n \cdot180^{\circ})$ , where $n$ is an integer.

STEP 2

We can use the periodic property of the tangent function to simplify the angle. We need to find an equivalent angle to $720^{\circ}$ that lies within the range $0^{\circ}$ to $180^{\circ}$ .
$720^{\circ} =4 \cdot180^{\circ}$

STEP 3

Since $720^{\circ}$ is a multiple of $180^{\circ}$ , we know that $\tan720^{\circ} = \tan0^{\circ}$ .

STEP 4

Now, we just need to find the value of $\tan0^{\circ}$ .

STEP 5

The value of $\tan0^{\circ}$ is0.
So, $\tan720^{\circ} =0$ .

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