Question

The domain of the tangent function is _____.

Short answer

The domain of the tangent function is the set of all real numbers, except the odd integer multiples of $\frac{\mathrm{\pi }}{2}$.

Step-by-step solution

Step 1. Given information.

We have:

The domain of the tangent function is _____.

Step 2. Fill the blank.

The tangent function, the x-coordinate of $P=\left(x,y\right)$can not be $0$since this results in division by $0.$

On the unit circle, there are two points $\left(0,1\right),\left(0,-1\right)$. These two points correspond to the angles $\frac{\mathrm{\pi }}{2}$and $\frac{3\mathrm{\pi }}{2}$.

Such angles must therefore be excluded from the domain of the tangent function.