Trigonometric calculations with bc

bc, the basic calculator under Linux and UNIX environments, provides commands for doing arbitrary precision mathematical calculations. The syntax for basic arithmetic functions is intuitive. Here, we look at the commands for doing trigonometric calculations.

Scale

The global scale variable gives the number of digits after the decimal point. By default, the value of scale is 0.

$ bc
bc 1.06.95
Copyright 1991-1994, 1997, 1998, 2000, 2004, 2006 Free Software Foundation, Inc.
This is free software with ABSOLUTELY NO WARRANTY.
For details type `warranty'. 
2/3
0
print scale, "\n"
0
scale=2
2/3
.66
scale=8
2/3
.66666666

Math functions

The math functions can be executed once bc is loaded with the math library, using the -l option. With the math library, the scale is, by default, set to 20. The mathematical functions are,

bc - Math functions
FunctionDescription
s (x)The sine of x, where x is in radians.
c (x)The cosine of x, where x is in radians.
a (x)The arctangent of x, The returned value is in radians.
l (x)The natural logarithm of x
e (x)The exponential function, raising e to the power x.
j (n, x)The Bessel function of integer order n of x.

The sine, cosine and arctangent functions work with angle arguments and return values in radians. However, angle values in radians are easily converted into degrees by noting that Π radians correspond to 180° and tan (45°) is 1. So to convert a value in radians into degrees, a factor of 180 / (4 * arctangent (1)) is to be multiplied to the value. For example,

$ bc -l
bc 1.06.95
Copyright 1991-1994, 1997, 1998, 2000, 2004, 2006 Free Software Foundation, Inc.
This is free software with ABSOLUTELY NO WARRANTY.
For details type `warranty'. 
a(768/1366)*180/(4*a(1))
29.34580364456776608792

The above calculation tells that the smaller angle of a right angled triangle with base 1366 units and height 768 units, which being the same as that of base, is 29.346°.