Solve $\sin A=\frac{\sqrt{3}}{-2}$ if $0 \leq A \leq \pi$
Answer
\(\boxed{\text{There is no solution to the equation } \sin A = \frac{\sqrt{3}}{-2} \text{ in the range } 0 \leq A \leq \pi}\)
Step 1 ：The given equation is \(\sin A = \frac{\sqrt{3}}{-2}\) with the range of A being \(0 \leq A \leq \pi\).
Step 2 ：The sine function is negative in the third and fourth quadrants. However, the given range for A is from 0 to \(\pi\), which includes the first and second quadrants. In these quadrants, the sine function is non-negative.
Step 3 ：Therefore, there is no solution to the equation \(\sin A = \frac{\sqrt{3}}{-2}\) in the given range.
Step 4 ：\(\boxed{\text{There is no solution to the equation } \sin A = \frac{\sqrt{3}}{-2} \text{ in the range } 0 \leq A \leq \pi}\)
