Maintenance script: Initial automated import

2016-02-24T18:15:52Z

Initial automated import

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{{Template:TI-BASIC:Command
|picture=SININVERSE.GIF
|summary=Returns the inverse sine (also called arcsine)
|syntax=sinֿ¹(''number'')
|location=Press:
# [2nd]
# [sinֿ¹]
|compatibility=TI-83/84/+/SE
|size=1 byte
}}

sinֿ¹( returns the [http://mathworld.wolfram.com/InverseSine.html arcsine] of its argument. It is the inverse of [[TI-BASIC:Sin|Sin(]], which means that sinֿ¹(z) produces an angle θ such that sin(θ)=z.

Like sin(, the result of sinֿ¹( depends on whether the calculator is in [[TI-BASIC:Radian_Mode|Radian]] or [[TI-BASIC:Degree_Mode|Degree]] mode. However, unlike sine, 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=sinֿ¹(n) from radians to degrees is θ*180/π and from degrees to radians is θ*π/180. The sinֿ¹( command also works on lists.

The sinֿ¹( function can be defined for all real and complex numbers; however, the function assumes real values only in the closed interval [-1,1]. Because the trigonometric functions and their inverses in the Z80 calculators are 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:

:sinֿ¹(1)
1.570796327

In degrees:

:sinֿ¹(1)
90

= Advanced Uses =

Since the function sine itself doesn't have the restrictions that arcsine does, and since arcsine is the inverse of sine, you can use sinֿ¹(sin( to keep a variable within a certain range (most useful on the [[TI-BASIC:Graphscreen|graph screen]]). Here is an example for a game like [[TI-BASIC:Pong|Pong]]. The ball travels between -6 and 6.

You could use a flag like this:

:If 6=abs(X \\ X is the position
:-D→D \\ D is the direction
:X+D→X \\ new position
:Pt-On(-54,X,"=")

An easier way to do this, without needing a flag or even an If statement, is using sinֿ¹(sin(

:X+1→X \\ Note: the calculator is in degree mode
:Pt-On(-54,sinֿ¹(sin(15X))/15,"=") \\ 15 is used because sinֿ¹ ranges from [-90,90]
and X from [-6,6], so 90/6=15

= Error Conditions =

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

= Related Commands =

* [[TI-BASIC:Sin|Sin(]]
* [[TI-BASIC:Cos|Cos(]]
* [[TI-BASIC:Arccos|cosֿ¹(]]
* [[TI-BASIC:Tan|Tan(]]
* [[TI-BASIC:Arctan|tanֿ¹(]][[Category:TI-BASIC]]
[[Category:TIBD]]

TI-BASIC:Arcsin - Revision history

Maintenance script: Initial automated import