evaluate. write your answer in simplified, rationalized form. do not round. tan 45° =

Explanation:

Step1: Recall tangent - sine/cosine

The tangent function is defined as $\tan\theta=\frac{\sin\theta}{\cos\theta}$. For $\theta = 45^{\circ}$, $\sin45^{\circ}=\frac{\sqrt{2}}{2}$ and $\cos45^{\circ}=\frac{\sqrt{2}}{2}$.

Step2: Calculate the value

$\tan45^{\circ}=\frac{\sin45^{\circ}}{\cos45^{\circ}}=\frac{\frac{\sqrt{2}}{2}}{\frac{\sqrt{2}}{2}} = 1$.

Answer:

$1$