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

Tangent(*expression*,*value*)

Press:

- 2nd PRGM to access the draw menu.
- 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 parabola X^{2} and then drawing a tangent line at the value X=2.

```
:"X²→Y₁
:Tangent(Y₁,2
```

or

`:Tangent(X²,2`

# Advanced Uses

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.

# Related Commands

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