Given $z = \frac{1}{2}\,\tan\left(\frac{a}{2}\right) \cdot q$, how can one express $a$ in terms of $z$?

Question

Probably an easy math problem I think.

I have the following expression:

$$\text{zoom} = \frac{1}{2}\,\tan\left(\frac{\text{angle}}{2}\right) \cdot q$$

How do I do the inverse? I.e. start with zoom and determine the value of angle?

Thanks.

Answer 1

To find Zoom from Angle, you make the following operations:

• Divide by $2$.
• Apply $\tan$ function
• Divide by $2$
• Multiply by $q$.

The inverse is made by applying the inverse operations in reverse order. That is, to find Angle from Zoom you make

• Divide by $q$
• Multiply by $2$
• Apply $\arctan$
• Multiply by $2$.

A teacher of mine said that the inverse of wearing the socks and then the shoes is taking off the shoes and then the socks.