# ATAN (Function)

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## V1Edit

Indications are, `BEEP`

in SmileBasic V1 is identical to that in V2.

## V2Edit

### ATAN (Number)Edit

`ATAN(number)`

returns the arctangent of the given number. The result is in radians, between approximately -pi/2 and approximately pi/2.

Note: `?(ATAN(1000)-PI()/2)*1000`

shows `0.244`

, indicating that `ATAN(value)`

can return a value greater than `PI()/2`

.

### ATAN (Numerator, Denominator)Edit

When `denominator`

is not zero, `ATAN(numerator, denominator)`

returns the arctangent of the fraction (numerator/denominator). The result is in radians, between approximately -pi and approximately pi.

When `denominator`

is zero and `numerator`

is zero, `ATAN(numerator, denominator)`

returns `0`

.

When `denominator`

is zero, and `numerator`

is positive, `ATAN(numerator, denominator)`

returns `1.57080078`

, which is slightly greater than pi/2. If I'm right about the fixed-point representation of values, this is `6434/4096`

.

When `denominator`

is zero, and `numerator`

is negative, `ATAN(numerator, denominator)`

returns `-1.57080078`

, which is slightly less than -pi/2. If I'm right about the fixed-point representation of values, this is `-6434/4096`

.

Note: `?(ATAN(0,-1)-PI)*1000`

shows `0.244`

, indicating the result can be greater than `PI()`

, and `?(ATAN(-1,-10000)+PI)*1000`

shows `-0.244`

, indicating the result can be less than `-PI()`

.

SmileBasic V2 does not have the inverse trigonometric functions, ASIN and ACOS. These functions can be calculated with the help of `ATAN`

, though. To calculate ASIN(S), use the expression `ATAN(S,SQR(1-S*S))`

. To calculate ACOS(C), use the expression `ATAN(SQR(1-C*C),C)`

. These expressions do not give very accurate results, however.

## V3Edit

Indications are, `ATAN`

in SmileBasic V3 is identical to that in V2. V3 **does** have `ASIN`

and `ACOS`

functions, and these will give more accurate results than the method described above.