Find Derivatives of Polar Equations with the TI-83 Plus

You can use the TI-83 Plus graphing calculator to find derivatives of polar equations. To find the derivative of a polar equation at a specified value of

follow these steps:

1. Graph the polar equation in a viewing window that contains the specified value of

   

   To get a viewing window containing the specified value of

   

   that value must be between

   

   and

   

2. Set the Format menu to ExprOn and CoordOn.

3. Press [2nd][TRACE] to access the Calculate menu.

4. Press [2] or [3] to respectively select the dy/dx or

   

   option.

5. If necessary, repeatedly press

   

   until the appropriate polar equation appears at the top of the screen.

6. Enter the specified value of

   

   To do so, use the keypad to enter the value of

   

   As you use the keypad,

   

   = replaces the coordinates of the cursor location appearing at the bottom of the screen in the previous step. The number you key in is placed after

   

   =. If you make a mistake when entering your number, press [CLEAR] and re-enter the number.

   If you’re interested only in finding the slope of the curve in a general area of the graph — instead of at a specific value of

   

   then just use the

   

   and

   

   to move the cursor to the desired location on the graph (instead of entering a value of

   

7. Press [ENTER].

   After pressing [ENTER], the derivative is displayed at the bottom of the screen.