Question

Solve for theta
y=cos(theta/2)

Answer 1

\[\theta=2\cos^{-1}(y)\]

Answer 2

They are the same thing, so it's true for all angles theta

Answer 3

The actual question itself has more components.
\[x=\sin \frac{ 1 }{ 2 }\theta, y=\cos \frac{ 1 }{ 2 }\theta\] I want to write it either in terms of y or x
\[\theta=2\cos^{-1}(y) \]\[x=\sin \frac{ 1 }{ 2 }*2\cos^{-1}(y)\]\[x=\sin(\cos^{-1}(y))\]

Answer 4

@larryboxaplenty what is true? o_o

Answer 5

Once we know theta can't we just plug it into x and simplify?

Answer 6

The question: "Eliminate the parameter to find a Cartesian equation of the curve"
\[-\pi \le \theta \le \pi\] then look up a few comments for the rest of the question xD

Answer 7

wait how did you get rid of sin and y?

Answer 8

wouldn't
\[x=\sqrt{1-y^2}\]

Answer 9

Yeah. I think it is.