Help finding a stationary point.

Question

$149-3\cos\left(\frac{t}{29}\right)+0.4\sin\left(\frac{2t}{9}\right) = M(t)$

I have the derivative as:

$\frac{3}{29}\sin\left(\frac{t}{29}\right)+\frac{4}{45}\cos\left(\frac{2t}{9}\right) = M'(t)$

I then equate it to $0$ but am having trouble solving for $t$.

$\frac{3}{29}\cos\left(90^\circ+\frac{t}{29}\right)+\frac{4}{45}\cos\left(\frac{2t}{9}\right)=0$

Please help

Thanks

Answer 1

Arguments are not multiple or submultiples. We cannot solve it analytically. Numerical methods (Newton-Raphson etc.) may need to be employed. The plot shows real negatives roots and many complex roots.