if SinA=1 divided by root 2 what's Sin2A
You asked:
Given \(\sin\left( A \right) = \frac{1}{\sqrt[2]{2}}\) evaluate the expression \(\sin\left( 2 A \right)\).
MathBot Answer:
The principal value in \(- \frac{\pi}{2} \le A \le \frac{\pi}{2}\) is \(A \approx 0.78539816\)
The real solutions are: \[\begin{aligned}A &= \left\{\frac{\pi \left(3 + 8 n\right)}{4}\; \middle|\; n \in \mathbb{Z}\right\} \approx \left\{6.2831853 n + 2.3561945\; \middle|\; n \in \mathbb{Z}\right\}\\A &= \left\{\frac{\pi \left(1 + 8 n\right)}{4}\; \middle|\; n \in \mathbb{Z}\right\} \approx \left\{6.2831853 n + 0.78539816\; \middle|\; n \in \mathbb{Z}\right\}\end{aligned}\]
By substituting the principal value into the expression, we find that: $$\begin{aligned}\sin{\left(2 A \right)} \approx 1.0\end{aligned}$$