Evaluate the trigonometric function at the quadrantal angle, or state that the expression is undefined. $$ \tan \frac{3 \pi}{2} $$

Question

UpStudy AI · Accepted Answer

1. Write the tangent function in terms of sine and cosine:
   $$
   \tan \frac{3\pi}{2} = \frac{\sin \frac{3\pi}{2}}{\cos \frac{3\pi}{2}}
   $$

2. Evaluate $$\sin \frac{3\pi}{2}$$ and $$\cos \frac{3\pi}{2}$$:
   - $$\sin \frac{3\pi}{2} = -1$$
   - $$\cos \frac{3\pi}{2} = 0$$

3. Substitute these values back into the expression:
   $$
   \tan \frac{3\pi}{2} = \frac{-1}{0}
   $$

4. Since division by zero is undefined, the expression is undefined.

Thus, $$\tan \frac{3\pi}{2}$$ is undefined.
$$\tan \frac{3\pi}{2}$$ is undefined.

Evaluate the trigonometric function at the quadrantal angle, or state that the expression is undefined. \[ \tan \frac{3 \pi}{2} \]