Question

find all solutions to the equation 2 cos0 +1=0

Answer 1

\[2\cos\theta+1=0.\]Is this what you mean?

Answer 2

yeass, i couldnt do the zero thingy

Answer 3

Well, let's do this by steps:

1. You're given: \(2\cos\theta+1=0\).
2. Our goal is to solve (1) for \(x\):
3. \(2\cos\theta=-1\),
4. \(\cos\theta=-1/2\),
5. \(\theta=\cos^{-1}(-1/2)=2\pi/3\)\[\]

Answer 4

Since \(\cos\theta\) is a periodic function with period \(2\pi\), our solutions will take the form \(\theta=2\pi n-2/3\pi\) and \(\theta=2\pi n+2/3\pi\) where \(n\in\mathbb{Z}\).\[\]