Property	Value
Hex Value	`$C5`
Categories	Catalog > C Keypad
Localizations	FR: `Arccos(`

`cos⁻¹(`

Overview

Returns arccosine of a real number, expression, or list.

Availability: Token available everywhere.

Syntax

cos⁻¹(value)

Arguments

Name	Type	Optional
⁻¹	real\|expression\|real[]
value	real\|expression\|real[]

Location

2nd, cos⁻¹

Description

cosֿ¹( returns the arccosine of its argument. It is the inverse of 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 Radian or 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 θ180/π and from degrees to radians is θπ/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 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 home screen). Here is an example for a game like 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 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

ERR:DOMAIN is thrown if you supplied an argument outside the interval [-1,1]
ERR:DATA TYPE is thrown if you input a complex value or a matrix.

Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan, Myles_Zadok, simplethinker, thornahawk.

History

Calculator	OS Version	Description
TI-82	1.0	`cos⁻¹` added
TI-83	0.01013	Renamed `cos⁻¹` to `cos⁻¹(`

Last update: September 30, 2023 15:38:51
Created: February 23, 2023 23:15:01

Authors: Adrien Bertrand

cos⁻¹(