Maintenance script: Automated superscript correction

2016-02-24T22:24:18Z

Automated superscript correction

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	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 [[TI-BASIC:System_Variables#equation\|equation variable]] (such as Y,,1,,) or an expression in terms of X (such as X²). Though you can use equation variables from any [[TI-BASIC:Graphing_Mode\|Graphing_Mode]], they will be treated as functions in terms of X. Tangent( also ignores the graphing mode currently selected.		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 [[TI-BASIC:System_Variables#equation\|equation variable]] (such as Y,,1,,) or an expression in terms of X (such as X²). Though you can use equation variables from any [[TI-BASIC:Graphing_Mode\|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] X^^2^^ and then drawing a tangent line at the value X=2.		Here is a simple example, where we are graphing the [wikipedia:parabola parabola] X<sup>2</sup> and then drawing a tangent line at the value X=2.

	:"X²→Y₁		:"X²→Y₁

Maintenance script: Initial automated import

2016-02-24T18:22:41Z

Initial automated import

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{{Template:TI-BASIC:Command
|picture=TANGENT.GIF
|summary=Draws a line tangent to an expression at the specified value.
|syntax=Tangent(''expression'',''value'')
|location=Press:
# 2nd PRGM to access the draw menu.
# 5 to select Tangent(, or use arrows and ENTER.
|compatibility=TI-83/84/+/SE
|size=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 [[TI-BASIC:System_Variables#equation|equation variable]] (such as Y,,1,,) or an expression in terms of X (such as X²). Though you can use equation variables from any [[TI-BASIC:Graphing_Mode|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] 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 [[TI-BASIC:Friendly_Window|friendly window]] to ensure it shows up as you intended.

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Tangent( will update X and Y for each coordinate drawn (like [[TI-BASIC:Drawf|DrawF]] and [[TI-BASIC:Drawinv|DrawInv]]), and exit with the last coordinate still stored.

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When evaluating the expression using Tangent(, the calculator will ignore the following errors: [[TI-BASIC:Errors#datatype|ERR:DATA TYPE]], [[TI-BASIC:Errors#divideby0|ERR:DIVIDE BY 0]], [[TI-BASIC:Errors#domain|ERR:DOMAIN]], [[TI-BASIC:Errors#increment|ERR:INCREMENT]], [[TI-BASIC:Errors#nonrealans|ERR:NONREAL ANS]], [[TI-BASIC:Errors#overflow|ERR:OVERFLOW]], and [[TI-BASIC:Errors#singularmat|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.

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Using [[TI-BASIC:Ans|Ans]] as an optimization for storing to an equation will not work. For example, the following code returns [[TI-BASIC:Errors#datatype|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 =

* '''[[TI-BASIC:Errors#invalid|ERR:INVALID]]''' is thrown if you try to use an equation variable that is undefined.

= Related Commands =

* [[TI-BASIC:Drawf|DrawF]]
* [[TI-BASIC:Drawinv|DrawInv]][[Category:TI-BASIC]]
[[Category:TIBD]]

TI-BASIC:Tangent - Revision history

Maintenance script: Automated superscript correction

Maintenance script: Initial automated import