Hi I was wondering if there is any algebraic way to find the zeroes of a cos/sin formula without using the unit circle?

Question

I understand how to find the zeroes using the unit circle or just graphing it for any matter for my equation.

I was just wondering if there is a formula or an algebraic way I could find them.

Here's the equation that I stumbled upon -3cos(x+pi/2),

Answer 1

I think you're asking if there's some formula akin to the quadratic formula that's used for equations of the form $y=ax^2+bx+c$, but in this case for $-3\cos(x-\frac\pi2)=0$.

No, not really. Andrew Hwang's comment is along the lines of what you should be thinking in this scenario. The unit circle is a good tool here as well.

You could come up with a formal approach for treating all equations of the type $\cos(ax-b)=0$. It'd be a good exercise. But memorizing the results in hopes of reapplying it isn't a useful way to approach related problem.

Perhaps you're interested in a formula that will solve any trigonometric equation? That'd be nice. Unfortunately, most equations in mathematics do not have neat algebraic solutions.