# ACOS¶

 Syntax ACOS (x) Location QL ROM

The function ACOS, is the arc-cosine function, that is to say the opposite to the cosine function (COS in SuperBASIC). However, x must always be in the range -1…1 as the cosine of an angle can only ever be in this range. Anything outside of this range will produce an Overflow Error.

The angle returned will be in the range 0…PI with ACOS(1)=0 and ACOS(-1)=PI. This means that the maximum angle which can be found with the ACOS function is 180 degrees. It is up to you to check whether this angle appears above or below the base line of the triangle (check the co-ordinates of the corners).

Note that if a negative value of x is provided, the angle returned will be the obtuse angle (ie. greater than 90 degrees).

Example

To calculate the angle at which a projectile was fired which has travelled a horizontal distance of 250 metres after 10 minutes and is travelling at 3 kilometres per hour (ignoring the effects of gravity):

```100 Speed=3:Distan=250/1000
110 Time_elapsed=10
120 Actual_distance=(Speed/60)*Time_elapsed
130 PRINT 'Projectile fired at an angle of ';
140 PRINT DEG(ACOS(Distan/Actual_distance))&' degrees'
```

NOTE

The angle returned will be in radians - if you wish to convert this angle to degrees, use DEG ( ACOS (x) ).

CROSS-REFERENCE