If n is an integer, n ∙ 180° represents an integer multiple of 180°, and (2n + 1) ∙ 90° represents an odd integer multiple of
90°. Decide whether the expression is equal to 0, 1, -1, or is undefined.
-$\tan \left( ( 2 n + 1 ) \cdot 90 ^ { \circ } \right)$
A) 1
B) 0
C) $- 1$
D) Undefined

Question

Quizplus · Accepted Answer

The expression $\tan \left( ( 2 n + 1 ) \cdot 90 ^ { \circ } \right)$ represents the tangent of an odd multiple of 90 degrees. Since $\tan(90^\circ)$ and $\tan(270^\circ)$ are undefined (as they correspond to points on the unit circle where the cosine value is 0, leading to division by zero in the tangent function), the expression is undefined.

If N Is an Integer, N ∙ 180° Represents an Integer