# How to transform equation and leave X alone

i need to transform this equation and leave x alone on the left, y and z bot on the right. like x = ... . Is it possible to do it? y and z are my variables. Also prefer $\pi$ to remain same if possible.

$$y = z\Bigg(0.5 - \frac{log\Big(\frac{1+\sin(x*\frac{\pi}{180})}{1-\sin(x*\frac{\pi}{180})}\Big)} {4 \pi}\Bigg)$$

Edit: I came up to this point, does this make any sense or am i just embarrass myself in front of you guys.

Removed my equation because it was wrong

If this is correct (I doubt it) how can i get rid of sin on the right hand side?

• what Kind of $\log$ is this? – Dr. Sonnhard Graubner Jul 13 '17 at 15:29
• @Dr.SonnhardGraubner i'm so sorry but couldn't understand what you mean. I'm not a math guy i'm afraid. Just trying to reverse a calculation used in a geographical calculation software program. – Ergec Jul 13 '17 at 15:33

hint

Let $a=\sin (\frac {x\pi}{180})$. $$b=\frac {1+a}{1-a}=-1+\frac {2}{1-a}$$

$$b=e^{4\pi (0,5-\frac {y}{z})}$$

$$a=1-\frac {2}{b+1}$$ $$x=\frac {180}{\pi}\arcsin (a)$$

• Thanks for the comment.. I edited my question and added what i did, hope it's correct. So now what's about sine? – Ergec Jul 13 '17 at 18:39
• @Ergec Your result is not correct. – hamam_Abdallah Jul 13 '17 at 22:29
• Hello, thanks for the final equation. But when i put my values into equation i don't get the expected result. Z = 256, Y = 101.26823920973 and for these two values X must have 35.152840 but it doesn't. – Ergec Jul 14 '17 at 9:30
• Is your logarithm Neperian or Decimal. May be you should replace 10 by e=2,7. – hamam_Abdallah Jul 14 '17 at 10:18
• This is brilliant :) seems it's e not 10 . You're a life saver, thanks a lot. – Ergec Jul 14 '17 at 10:38