how do you find the value of theta given tan theta is 0.01/130
You asked:
Solve the equation \(\tan\left( θ \right) = \frac{0.01}{130}\) for the variable \(θ\).
MathBot Answer:
The principal value in \(- \frac{\pi}{2} < θ < \frac{\pi}{2}\) is \(θ \approx 7.6923077 \cdot 10^{-5}\)
The real solutions are: \[\begin{aligned}θ &= \left\{2 \pi n + \arctan{\left(\frac{1}{13000} \right)}\; \middle|\; n \in \mathbb{Z}\right\} \approx \left\{6.2831853 n + 7.6923077 \cdot 10^{-5}\; \middle|\; n \in \mathbb{Z}\right\}\\θ &= \left\{\pi + 2 \pi n + \arctan{\left(\frac{1}{13000} \right)}\; \middle|\; n \in \mathbb{Z}\right\} \approx \left\{6.2831853 n + 3.1416696\; \middle|\; n \in \mathbb{Z}\right\}\end{aligned}\]