# Implicit function plot in Mathematica

• Mathematica
freefaller
Hello everyone,

I have an implicit equation:
$$-155.034 x^4 ×sin(377 t) = 0.0524166 x^6 × cos^{1.414}(-377t)-(0.0581964+0.0442696 i) x ×cos^4(377 t)+7.09332 cos^5(377 t)$$
I would like to create a plot of this function using Mathematica, but I am not very proficient with this software, and the little I know is just what I could teach myself.

So I tried something like this:

ContourPlot[-155.034 x^4 Sin[
377 t] == (0.139677 x^6 Cos[377 t]^1.414 - (0.0581964 +
0.0442696 I) x Cos[377 t]^4 + 7.09332 Cos[377 t]^5), {t, 0,
2}, {x, -4, 4}]

But with no result. I got a blank plot and sometimes a few errors after i tried again.

How would I be able to get this graph?
Thank you.

## Answers and Replies

Bill Simpson
Assuming x and t are Real, the left hand side of your equality will always be Real, but the right hand side of your equality will be Complex everywhere except when x==0 or t==1/377(Pi/2+2n Pi) or t==1/377(-Pi/2+2n Pi) for Integer n. But when t is any one of those values then the right hand side is zero and you end up with 155.034x^4==0

With that insight can you think how you might change what you want to do?

freefaller
You're right, i did the math again through mathematica and i got a slightly different equation:
$$-\frac{2436.77 Sin[377 t]}{x^{0.8285} Cos[377 t]^{0.1715}} = 170 x Cos[377 t] + \frac{5.24172 Cos[377 t]^{3.314}}{ x^{3.314}} - \frac{232.031 Cos[377 t]^{4.1425}}{ x^{4.1425}}$$
This is not the result i wanted though. i'll start another thread so that i can make sure my math was correct.