Q. 6 - Precalculus Enhanced with Graphing Utilities

Question

The domain of the tangent function is _____.

Step-by-Step Solution

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 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.