# SINE(angle) in degrees.
# Called as:
# Sin ANGLE
# Where ANGLE is any positive floating point value.
# Returns SIN as a variable to 8 decimal places.
# Google sin(degrees) values for first quadrant.
#
# 0	0.00000000000
# 15	0.25881904510
# 30	0.50000000000
# 45	0.70710678118
# 60	0.86602540378
# 75	0.96592582628
# 90	1.00000000000
Sin()
{
	# SIN fixed to 8 decimal places.
	ANGLE=$1
	while [ $ANGLE -gt 360.0 ]
	do
		ANGLE=$(( $ANGLE-360.0 ))
	done
	if [ $ANGLE -ge 360.0 ]
	then
		ANGLE=0.0
	fi
	if [ $ANGLE -gt 270.0 ]
	then
		ANGLE=$(( $ANGLE-360.0 ))
	fi
	if [ $ANGLE -gt 180.0 ]
	then
		ANGLE=$(( -($ANGLE-180.0) ))
	fi
	if [ $ANGLE -gt 90.0 ]
	then
		ANGLE=$(( 180.0-$ANGLE ))
	fi
	Radian $ANGLE
	SIN=$(( $RADIAN-(($RADIAN**3)/6.0)+(($RADIAN**5)/120.0)-(($RADIAN**7)/5040.0)+(($RADIAN**9)/362880.0)-(($RADIAN**11)/39916800.0)+(($RADIAN**13)/6227020800.0) ))
	SIN=$( printf "%.8f" "$SIN" )
}

#Sin(radians).
#{
#	RADIAN=$1
#	while [ $RADIAN -gt $(( 2*$PI )) ]
#	do
#		RADIAN=$(( $RADIAN-2*$PI ))
#	done
#	if [ $RADIAN -ge $(( 2*$PI )) ]
#	then
#		RADIAN=0.0
#	fi
#	if [ $RADIAN -gt $(( (3*PI)/4 )) ]
#	then
#		RADIAN=$(( $RADIAN-2*PI ))
#	fi
#	if [ $RADIAN -gt $PI ]
#	then
#		RADIAN=$(( -($RADIAN-$PI) ))
#	fi
#	if [ $RADIAN -gt $(( $PI/2 )) ]
#	then
#		RADIAN=$(( $PI-$RADIAN ))
#	fi
#	SIN=$(( $RADIAN-(($RADIAN**3)/6.0)+(($RADIAN**5)/120.0)-(($RADIAN**7)/5040.0)+(($RADIAN**9)/362880.0)-(($RADIAN**11)/39916800.0)+(($RADIAN**13)/6227020800.0) ))
#}


# COSINE(x)
# Called as:
# Cos RADIANS
# Returns COS as a variable.
Cos()
{
	:
}

# ANGLE to RADIAN.
# Called as:
# Radian ANGLE
# Returns RADIAN as a variable.
Radian()
{
	ANGLE=$1
	RADIAN=$(( ($ANGLE*$PI)/180.0 ))
}

# RADIAN to ANGLE.
# Called as:
# Angle RADIAN
# Returns ANGLE as a variable.
Angle()
{
	RADIAN=$1
	ANGLE=$(( ($RADIAN*180.0)/$PI ))
}

# **********************************
# Test radians.
#for x in $( seq 0 $(( $PI/12 )) $(( 6*PI )) )
#do
#	Sin x
#	printf "%u -> %.8f\n" "$x" "$SIN"
#done

# Test degrees.
for x in $( seq 0.0 15.0 360.0 )
do
	Sin x
	echo "$x -> $SIN"
done
# **********************************

Last login: Thu Oct 18 15:52:22 on ttys000
AMIGA:amiga~> cd Desktop/Code/Shell
AMIGA:amiga~/Desktop/Code/Shell> ./ksh_math.sh
0 -> 0.00000000
15 -> 0.25881905
30 -> 0.50000000
45 -> 0.70710678
60 -> 0.86602540
75 -> 0.96592583
90 -> 1.00000000
105 -> 0.96592583
120 -> 0.86602540
135 -> 0.70710678
150 -> 0.50000000
165 -> 0.25881905
180 -> 0.00000000
195 -> -0.25881905
210 -> -0.50000000
225 -> -0.70710678
240 -> -0.86602540
255 -> -0.96592583
270 -> -1.00000000
285 -> -0.96592583
300 -> -0.86602540
315 -> -0.70710678
330 -> -0.50000000
345 -> -0.25881905
360 -> 0.00000000
AMIGA:amiga~/Desktop/Code/Shell> _