Question

Simple question about trigonometry, the tangent function. Need to draw a picture first.

Answer 1

\[\tan \theta = \frac{ x }{ r }\]
\[\tan \frac{ \theta }{ 2 } = \frac{ x }{ 2r }\]

I know the first two are true, but is this also true?
\[\tan \frac{ \theta }{ 3 } = \frac{ x }{ 3r }\]

Answer 2

If not, tangent of what angle is equal to x/3r?

Answer 3

Is that drawing for a specific value of theta or a general statement?
tan(30) is not half of tan(60). How are the first two true?

Answer 4

Somehow I messed myself up by thinking about this, give me a second to figure out what my real question/drawing is. lol

Answer 5

Ok, my real question must be:

\[\phi=\tan^{-1}(\frac{ 1 }{ 2 }\tan( \theta))\]

Is there a nice way to write phi in terms of theta other than this?

Answer 6

Sorry, which angle is phi?

Answer 7

\[\tan^{-1}(\frac{ 1 }{ 2 }\tan( \theta))\] This whole expression is what I'm looking to represent as something better.