cos(40t) = -(1/2)sin(40t)
You asked:
Solve the equation \(\cos\left( 40 t \right) = -\left( \frac{1}{2} \sin\left( 40 t \right) \right)\) for the variable \(t\).
MathBot Answer:
The real solutions are: \[\begin{aligned}t &= \left\{- \frac{\arctan{\left(2 \right)}}{40} + \frac{\pi}{40} + \frac{\pi n}{20}\; \middle|\; n \in \mathbb{Z}\right\} \approx \left\{0.15707963 n + 0.050861098\; \middle|\; n \in \mathbb{Z}\right\}\\t &= \left\{- \frac{\arctan{\left(2 \right)}}{40} + \frac{\pi}{20} + \frac{\pi n}{20}\; \middle|\; n \in \mathbb{Z}\right\} \approx \left\{0.15707963 n + 0.12940091\; \middle|\; n \in \mathbb{Z}\right\}\end{aligned}\]