if cosA = sqrt(3)/2 then what is cotA
You asked:
Given \(\cos\left( A \right) = \frac{\sqrt{3}}{2}\) evaluate the expression \(\cot\left( A \right)\).
MathBot Answer:
The principal value in \(0 \le A \le \pi\) is \(A \approx 0.52359878\)
The real solutions are: \[\begin{aligned}A &= \left\{\frac{\pi \left(11 + 12 n\right)}{6}\; \middle|\; n \in \mathbb{Z}\right\} \approx \left\{6.2831853 n + 5.7595865\; \middle|\; n \in \mathbb{Z}\right\}\\A &= \left\{\frac{\pi \left(1 + 12 n\right)}{6}\; \middle|\; n \in \mathbb{Z}\right\} \approx \left\{6.2831853 n + 0.52359878\; \middle|\; n \in \mathbb{Z}\right\}\end{aligned}\]
By substituting the principal value into the expression, we find that: $$\begin{aligned}\cot{\left(A \right)} \approx 1.7320508\end{aligned}$$