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I have the following quantity:

c_p = 1 - (4*sin(th)^2+2*5*sin(th)/pi+(5/(2*pi))^2)

and I am trying to find its roots (the solutions for c_p==0).

When plotting c_p as a function of th between $-\pi$ and $\pi$, I can see the curve crosses the x-axis at four positions. However, solve(c_p==0, th) is only giving two roots: $$\left[{theta} = -\arcsin\left(\frac{5}{4 \ \pi} + \frac{1}{2}\right),\quad {theta} = -\arcsin\left(\frac{5}{4 \ \pi} - \frac{1}{2}\right)\right].$$ It appears that solve can only find the roots that are in the domain of the $\arcsin$ function, i.e in the interval $[-\pi, \pi]$. Is there a way to get the other two roots?

I have the following quantity:

c_p = 1 - (4*sin(th)^2+2*5*sin(th)/pi+(5/(2*pi))^2)

and I am trying to find its roots (the solutions for c_p==0).

When plotting c_p as a function of th between $-\pi$ and $\pi$, I can see the curve crosses the x-axis at four positions. However, solve(c_p==0, th) is only giving two roots: $$\left[{theta} = -\arcsin\left(\frac{5}{4 \ \pi} + \frac{1}{2}\right),\quad {theta} = -\arcsin\left(\frac{5}{4 \ \pi} - \frac{1}{2}\right)\right].$$ It appears that solve can only find the roots that are in the domain of the $\arcsin$ function, i.e in the interval $[-\pi, \pi]$. $[-\pi/2, \pi/2]$. Is there a way to get the other two roots?

I have the following quantity:

c_p = 1 - (4*sin(th)^2+2*5*sin(th)/pi+(5/(2*pi))^2)

and I am trying to find its roots (the solutions for c_p==0).

When plotting c_p as a function of th between $-\pi$ and $\pi$, I can see the curve crosses the x-axis at four positions. However, solve(c_p==0, th) is only giving two roots: $$\left[{theta} = -\arcsin\left(\frac{5}{4 \ \pi} + \frac{1}{2}\right),\quad {theta} = -\arcsin\left(\frac{5}{4 \ \pi} - \frac{1}{2}\right)\right].$$ It appears that solve can only find the roots that are in the domain of the $\arcsin$ function, i.e in the interval $[-\pi/2, \pi/2]$. $[-\dfrac{\pi}{2},\dfrac{\pi}{2}]$. Is there a way to get the other two roots?

I have the following quantity:

c_p = 1 - (4*sin(th)^2+2*5*sin(th)/pi+(5/(2*pi))^2)

and I am trying to find its roots (the solutions for c_p==0).

When plotting c_p as a function of th between $-\pi$ and $\pi$, I can see the curve crosses the x-axis at four positions. However, solve(c_p==0, th) is only giving two roots: $$\left[{theta} $$\left[theta = -\arcsin\left(\frac{5}{4 \ \pi} + \frac{1}{2}\right),\quad {theta} theta = -\arcsin\left(\frac{5}{4 \ \pi} - \frac{1}{2}\right)\right].$$ It appears that solve can only find the roots that are in the domain of the $\arcsin$ function, i.e in the interval $[-\dfrac{\pi}{2},\dfrac{\pi}{2}]$. Is there a way to get the other two roots?