Find t such that - $\frac { \pi } { 2 }$ ≤ t ≤ $\frac { \pi } { 2 }$ and sin t = sin $\left( \frac { 3 \pi } { 4 } \right)$ .
A) $\frac { \pi } { 2 }$
B) $\frac { \pi } { 4 }$
C) $\frac { \pi } { 6 }$
D) - $\frac { \pi } { 3 }$
E) none of these

Question

Quizplus · Accepted Answer

The sine function has the property that $\sin(x) = \sin(\pi - x)$. Given $\sin\left(\frac{3\pi}{4}\right)$, we can find that $\sin\left(\frac{\pi}{4}\right)$ will have the same value because $\frac{3\pi}{4}$ and $\frac{\pi}{4}$ are supplementary angles (their sum equals $\pi$). Since $\frac{\pi}{4}$ is within the given range $-\frac{\pi}{2} \leq t \leq \frac{\pi}{2}$, it is the correct answer.

Find T Such That - π2\frac { \pi } { 2 }2π​

Find T Such That - $\frac { \pi } { 2 }$