Question
Evaluate the trigonometric function at the quadrantal angle, or state that the expression is undefined. \[ \tan \frac{3 \pi}{2} \]
Ask by Martin Griffin. in the United States
Mar 10,2025
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Answer
\(\tan \frac{3\pi}{2}\) is undefined.
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The angle \( \frac{3 \pi}{2} \) radians corresponds to 270 degrees, which is located on the negative y-axis in the unit circle. At this angle, the tangent function, defined as \( \tan \theta = \frac{\sin \theta}{\cos \theta} \), is evaluated as follows: Here, \(\sin \frac{3\pi}{2} = -1\) and \(\cos \frac{3\pi}{2} = 0\). Since we cannot divide by zero, \( \tan \frac{3 \pi}{2} \) is undefined. Thus, the answer is that the expression is undefined.