# TI-BASIC:Tangent

Command Summary

Draws a line tangent to an expression at the specified value.

Command Syntax

Tangent(expression,value)

Press:

1. 2nd PRGM to access the draw menu.
2. 5 to select Tangent(, or use arrows and ENTER.

TI-83/84/+/SE

1 byte

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 Y,,1,,) 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 [wikipedia:parabola parabola] X2 and then drawing a tangent line at the value X=2.

```:"X²→Y₁
:Tangent(Y₁,2
```

or

```:Tangent(X²,2
```

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.

Tangent( will update X and Y for each coordinate drawn (like DrawF and DrawInv), and exit with the last coordinate still stored.

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.

Using Ans as an optimization for storing to an equation will not work. For example, the following code returns ERR:DATA TYPE because Ans is a string, not an equation variable.

```:"X²
:Tangent(Ans,2
```

Of course, you can use Ans in the equation, if it's a real number, but that's usually not as useful.

# Error Conditions

• ERR:INVALID is thrown if you try to use an equation variable that is undefined.