h=L*tan(a)*d-(.5g*(d^2)*(cos(a)^-2)*(L^-2)) that is a range equation. I don't know enough properties about trigonomerty to separate "a" or "theta". I don't know any calculus identities that I can apply here. It would be of great help if you could find "a". All other letters above are instantaneous constants that are known throughout the projectile's trajectory. Thank you in advance.
As a heads up, the constants are variables because some do change at different times. But they are not relevant.
+118723 h=L*tan(a)*d-(.5g*(d^2)*(cos(a)^-2)*(L^-2))
Lets try to make sense of this.
\(h=L*tan(a)*d-(.5g*(d^2)*(cos(a)^{-2})*(L^{-2}))\\ h=Ld*tan(a)\quad-[0.5gd^2cos(a)^{-2})*(L^{-2})]\\ h=Ld*tan(a)\quad-[0.5gd^2cos(\frac{1}{a^{2}})*(\frac{1}{L^{2}})]\\ h=Ld\;tan(a)\quad-\frac{gd^2cos(\frac{1}{a^{2}})}{2L^2}\\ \)
At this point I need to ask, did you intend cos(a^-2) like I have done
or
did you intend (cos(a))^-2
The meaning is not clear. :(
Is the rest correct, I mean is it what you are asking?
