Maximum Y-Coordinate Values Of A Cardioid

Algebraically determine the maximum value of the y-coordinate of points on the cardioid for 0 ≤ θ ≤ π.

I used the formula:

, which yielded .

If I solve , setting it to zero, it will give the value of theta at which horizontal tangents exist. The problem is that I don't know how to solve it.

After graphing it, I know that the max value occurs when and , but I'm not sure how to get to those values.

Re: Maximum Y-Coordinate Values Of A Cardioid

All you need is that

Now we have

Setting equal to zero and factoring gives

This will give you both the max and min values.

Re: Maximum Y-Coordinate Values Of A Cardioid

Wow, that's so much better than my inchoate solution.

Thanks a lot!

Re: Maximum Y-Coordinate Values Of A Cardioid