Question

evaluate the trigonometric function at the quadrantal angle, or state that the expression is undefined. tan\frac{3\pi}{2} select the correct choice below and, if necessary, fill in the answer box to complete your choice. oa. tan\frac{3\pi}{2}= ob. the expression is undefined.

Explanation:

Step1: Recall the definition of tangent

The tangent function is defined as $\tan\theta = \frac{\sin\theta}{\cos\theta}$.

Step2: Find $\sin\frac{3\pi}{2}$ and $\cos\frac{3\pi}{2}$

We know that $\sin\frac{3\pi}{2} = - 1$ and $\cos\frac{3\pi}{2}=0$.

Step3: Substitute into the tangent formula

Substitute $\theta=\frac{3\pi}{2}$ into $\tan\theta=\frac{\sin\theta}{\cos\theta}$, we get $\tan\frac{3\pi}{2}=\frac{\sin\frac{3\pi}{2}}{\cos\frac{3\pi}{2}}=\frac{- 1}{0}$. Division by zero is undefined in mathematics.

Answer:

B. The expression is undefined.