Evaluate.
-$$\sin \left( \frac { 2,222,033 \pi } { 2 } \right)$$
A) 0
B) 1
C) $\frac { 1 } { 2 }$
D) $- 1$

Question

Quizplus · Accepted Answer

The sine function has a period of $2\pi$, so we can simplify the expression by considering the argument modulo $2\pi$. However, since we're dealing with a half-integer multiple of $\pi$, we only need to recognize that $\sin\left(\frac{\pi}{2}\right) = 1$, and any odd multiple of $\frac{\pi}{2}$ will also result in $\sin$ being 1, as long as it's in the form of $(4n + 1)\frac{\pi}{2}$ for integer $n$. Since $2,222,033$ is an odd number, it fits this form, leading to a sine value of 1.

Evaluate - sin⁡(2,222,033π2)\sin \left( \frac { 2,222,033 \pi } { 2 } \right)sin(22,222,033π​)

Evaluate
- $\sin \left( \frac { 2,222,033 \pi } { 2 } \right)$