Question

How do I find the value of $\tan \left(225°\right)$.

Answer 1

Find the value of $\tan \left(225°\right)$:

First, determine the sign of $\tan \left(225°\right)$.

$225°$ can be rewritten as $225°=180°+45°=\left(2\times 90°\right)+45°$.

Thus $225°$ belongs to the third quadrant.

It is known that the values of tangents are positive $\left(+\right)$ in the third quadrant.

It is also known that, $\mathbf{tan}\mathbf{(}\mathbf{180}\mathbf{°}\mathbf{+}\mathbf{x}\mathbf{°}\mathbf{)}\mathbf{=}\mathbf{tan}\mathbf{(}\mathbf{x}\mathbf{°}\mathbf{)}$.

Thus, $\tan \left(225°\right)=\tan \left(180°+45°\right)=\tan \left(45°\right)=1$.

Therefore, the value of $\tan \left(225°\right)$ is $1$.