S-curve Graph Mirror

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I have an s-curve equation that uses cosine. Any trigonometric function is allowed but I can't use exponential or logarithmic equations as they don't perform to what is required. The cosine equation works great for certain settings but for others, I need to mirror it using the existing coordinate points; I need to invert the ess while using the same coordinate points. I've tried a few ways but I can't have the equation switching its location to a different quadrant. The included image, or link, shows the equation, the current s-curve in red, and the needed s-curve in green. Please help me to find the variation of the current equation or a different trigonometric equation that will enable this. Thank you. Gary

S-curve equation and graph, current s-curve in red, needed s-curve in green