Question

Need help remembering how I solve for theta for arctan(theta) = (cos(phi))/2

Answer 1

\[\arctan(\theta) = \frac{ \cos(\phi) }{ 2 }\]

solve for theta

Answer 2

take the tangent of both sides?
\[\arctan(\theta) = \frac{\cos(\phi)}{2}\]\[\tan(\arctan(\theta)) = \tan\left(\frac{\cos(\phi)}{2}\right)\]\[\theta=\tan \left( \frac{ \cos \phi }{ 2 } \right)\]

Answer 3

dont think that's it. because inverse of tangent is cotangent

Answer 4

that's the same thing I did.

Answer 5

That's it. Cotangent is the reciprocal of tangent, not the inverse. Arctan is defined such that
\[\arctan(\tan(x)) = x\] Consequently: \[\tan(\arctan(x)) = x\]

Answer 6

ok i appreciate it.