The Tangent( command draws a graph of an expression and then draws a line tangent to that expression, with the line touching the graph at the point of the specified value. You can either use a equation variable (such as Y1) or an expression in terms of X (such as X²). Though you can use equation variables from any graphing mode, they will be treated as functions in terms of X. Tangent( also ignores the graphing mode currently selected.
Here is a simple example, where we are graphing the parabola X2 and then drawing a tangent line at the value X=2.
Whether the graph shows up or not is dependent on the window dimensions of the graph screen, and you should use a friendly window to ensure it shows up as you intended.
When evaluating the expression using Tangent(, the calculator will ignore the following errors: ERR:DATA TYPE, ERR:DIVIDE BY 0, ERR:DOMAIN, ERR:INCREMENT, ERR:NONREAL ANS, ERR:OVERFLOW, and ERR:SINGULAR MAT. If one of these errors occurs, the data point will be omitted. However, the errors will still be thrown if they occur when evaluating the function at the point of tangency.
Of course, you can use Ans in the equation, if it's a real number, but that's usually not as useful.
- ERR:INVALID is thrown if you try to use an equation variable that is undefined.