If sinA= 1/3 find the value of cosecA
You asked:
Given \(\sin\left( A \right) = \frac{1}{3}\) evaluate the expression \(\csc\left( A \right)\).
MathBot Answer:
The principal value in \(- \frac{\pi}{2} \le A \le \frac{\pi}{2}\) is \(A \approx 0.33983691\)
The real solutions are: \[\begin{aligned}A &= \left\{2 \pi n + \arctan{\left(\frac{\sqrt{2}}{4} \right)}\; \middle|\; n \in \mathbb{Z}\right\} \approx \left\{6.2831853 n + 0.33983691\; \middle|\; n \in \mathbb{Z}\right\}\\A &= \left\{\pi - \arctan{\left(\frac{\sqrt{2}}{4} \right)} + 2 \pi n\; \middle|\; n \in \mathbb{Z}\right\} \approx \left\{6.2831853 n + 2.8017557\; \middle|\; n \in \mathbb{Z}\right\}\end{aligned}\]
By substituting the principal value into the expression, we find that: $$\begin{aligned}\csc{\left(A \right)} \approx 3.0\end{aligned}$$