Maintenance script: Initial automated import

2016-02-24T18:34:19Z

Initial automated import

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{{Template:TI-BASIC:Command
|picture=COSINVERSE.GIF
|summary=Returns the inverse cosine (also called arccosine)
|syntax=cosֿ¹(''number'')
|location=Press:
# [2nd]
# [cosֿ¹]
|compatibility=TI-83/84/+/SE
|size=1 byte
}}

cosֿ¹( returns the [http://mathworld.wolfram.com/InverseCosine.html arccosine] of its argument. It is the inverse of [[TI-BASIC:Cos|Cos(]], which means that cosֿ¹(n) produces an angle θ such that cos(θ)=n.

Like cos(, the result of cosֿ¹( depends on whether the calculator is in [[TI-BASIC:Radian_Mode|Radian]] or [[TI-BASIC:Degree_Mode|Degree]] mode. However, unlike cosine, the result is in degrees or radians, not the argument. A full rotation around a circle is 2π radians, which is equal to 360°. The conversion of θ=cosֿ¹(n) from radians to degrees is θ*180/π and from degrees to radians is θ*π/180. The cosֿ¹( command also works on a list.

The cosֿ¹( function can be defined for all real and complex numbers, but assumes real values only in the closed interval [-1,1]. Because Z80 calculators have their trigonometric functions and inverses restricted only to real values, the calculator will throw [[TI-BASIC:Errors#domain|ERR:DOMAIN]] if the argument is outside of this interval, no matter what the mode setting may be.

In radians:

:cosֿ¹(-1)
3.141592654

In degrees:

:cosֿ¹(-1)
180

= Advanced Uses =

Since the function cosine itself doesn't have the restrictions that arccosine does, and since arccosine is the inverse of cosine, you can use cosֿ¹(cos( to keep a variable within a certain range (most useful for the [[TI-BASIC:Homescreen|home screen]]). Here is an example for a game like [[TI-BASIC:Pong|Pong]]. The ball travels between 0 and 12.

You could use a flag like this:

:If X=12 or not(X \\ X is the position
:-D→D \\ D is the direction
:X+D→X \\ new position
:Output(8,X,"=

An easier way to do this, without needing a flag or even an [[TI-BASIC:If|If]] statement, is using cosֿ¹(cos(

:X+1→X \\ Note: the calculator is in Degree mode
:Output(8,cosֿ¹(cos(15X))/15,"=") \\ I used 15 because cosֿ¹ ranges from [0,180]
and X from [0,12], so 180/12=15

= Error Conditions =

* '''[[TI-BASIC:Errors#domain|ERR:DOMAIN]]''' is thrown if you supplied an argument outside the interval [-1,1]
* '''[[TI-BASIC:Errors#datatype|ERR:DATA TYPE]]''' is thrown if you input a complex value or a matrix.

= Related Commands =

* [[TI-BASIC:Sin|Sin(]]
* [[TI-BASIC:Arcsin|sinֿ¹(]]
* [[TI-BASIC:Cos|Cos(]]
* [[TI-BASIC:Tan|Tan(]]
* [[TI-BASIC:Arctan|tanֿ¹(]][[Category:TI-BASIC]]
[[Category:TIBD]]

TI-BASIC:Arccos - Revision history

Maintenance script: Initial automated import