# How to make lowest part of this curve follow straight line instead sine wave?

https://www.desmos.com/calculator/xgw33pnx1p

When moving the slider of variable "m", we can see that the red curve is being bend, and you can clearly see that the lowest part of that red curve follow sine wave (green line)

Instead follow sine wave, how to make that lowest part follow blue line (straight line) instead sine wave while changing "m" variable and still keep original shape? If you know how, please explain as simple as possible how did it work and provide the polar function :(.

I know that this question may asked somewhere, but with limit English, I don't know how to search this type of problem and the name of the curve, and the question may unclear to some...

• Forgot to cite: variable "m" is within range 0 <= m <= 1, for not creating more than 2 petals, sorry for confusion. And the lowest part (should I call it "tipped point") should be within y-axis... Sep 20, 2017 at 6:17

The green line is NOT a part of the red curve. It is the drawing of a different function.

You can see on the left side of the figure the equations of three different functions, which are respectively drawn in red, green and blue.

The red curve is the is the drawing in polar coordinates. When you change the value of $m$, of course the chape changes, but not as you imagine. You wrote "The red curve is being bend". This because you make $m$ vary only on a small range. Try on a larger range and see what append. For example $m=1.5$ then $m=5$ on the figures below.

The green curve is not "the lowest part of the red curve" as you wrote. It represents a pure sinusoidal function. The change of $m$ translate it, nothing more.

The blue curve represents a linear function. The change of $m$ translate it, that's all.

Drawing the three functions is only a feature of the software that you use. The question "How to make lowest part of this curve follow straight line instead sine wave?" is a non-sens.

The Cartesian coordinates of the "tipped point" are $\left(x=0\:,\:y=\cos(m\frac{\pi}{2})\right)$. If you want that this point follows a moving straight line (drawn in blue), just change the equation of the straight line to : $$y=\left(-x+\cos(m\frac{\pi}{2}) \right)d$$