The tangent function is defined as the ratio of the sine to the cosine of the angle.
For \( 270^\circ \):
- The sine of \( 270^\circ \) is \( \sin(270^\circ) = -1 \).
- The cosine of \( 270^\circ \) is \( \cos(270^\circ) = 0 \).
Since the tangent function is given by:
\[ \tan(\theta) = \frac{\sin(\theta)}{\cos(\theta)} \]
we can plug in the values:
\[ \tan(270^\circ) = \frac{\sin(270^\circ)}{\cos(270^\circ)} = \frac{-1}{0} \]
Since division by zero is undefined, we conclude that:
\[ \tan(270^\circ) \text{ is undefined.} \]
2 answers