# (30) Trigonometric functions plotted in graph mode¶

Next, we continue with a simple mathematical illustration of sine and cosine, highlighting the graph mode for linear projections and the new curved vectors for angles.

The script simply draws a graph basemap, computes sine and cosine and plots them as lines, then indicates on a circle that these quantities are simply the projections of an unit vector on the x- and y-axis, at the given angle.

#!/usr/bin/env bash
#		GMT EXAMPLE 30
#
# Purpose:	Show graph mode and math angles
# GMT modules:	gmtmath, basemap, text and plot
# Unix progs:	echo, rm
#
# Draw generic x-y axes with arrows
gmt begin ex30
gmt basemap -R0/360/-1.25/1.75 -JX20c/15c -Bx90f30+u@. -By1g10 -BWS+t"Two Trigonometric Functions" \
--MAP_FRAME_TYPE=graph --MAP_VECTOR_SHAPE=0.5

# Draw sine an cosine curves
gmt math -T0/360/0.1 T COSD = | gmt plot -W3p
gmt math -T0/360/0.1 T SIND = | gmt plot -W3p,0_6 --PS_LINE_CAP=round

# Indicate the x-angle = 120 degrees
gmt plot -W0.5p,- <<- EOF
120	-1.25
120	1.25
EOF

gmt text -Dj0.2c -N -F+f+j <<- EOF
360 1 18p,Times-Roman RB x = cos(@%12%a@%%)
360 0 18p,Times-Roman RB y = sin(@%12%a@%%)
120 -1.25 14p,Times-Roman LB 120@.
370 -1.35 24p,Symbol LT a
-5 1.85 24p,Times-Roman RT x,y
EOF

# Draw a circle and indicate the 0-70 degree angle
echo 0 0 | gmt plot -R-1/1/-1/1 -Jx3.8c -X9c -Y7c -Sc5c -W1p -N
gmt plot -W1p <<- EOF
> x-gridline  -Wdefault
-1	0
1	0
> y-gridline  -Wdefault
0	-1
0	1
> angle = 0
0	0
1	0
> angle = 120
0	0
-0.5	0.866025
> x-gmt projection -W2p
-0.3333	0
0	0
> y-gmt projection -W2p
-0.3333	0.57735
-0.3333	0
EOF

gmt text -Dj4p -F+f+a+j <<- EOF
-0.16666 0 12p,Times-Roman 0 CT x
-0.3333 0.2888675 12p,Times-Roman 0 RM y
0.22 0.27 12p,Symbol -30 CB a
-0.33333 0.6 12p,Times-Roman 30 LB 120@.
EOF

echo 0 0 1.25c 0 120 | gmt plot -Sm0.4c+e -W1p -Gblack
gmt end show Trigonometric functions plotted in graph mode.