### Gnuplot R language and Zim with Calculus

The plotting language is a little bit different, but it sinks in after while and there is a method to the insanity. In this case I am just illustrating the example used in the MIT lectures on Trapezoidal approximation. I learned how to use different characters and symbols for axis as well as points and labels besides getting to go through the idea of areas under curves as boxes that get tinier and tinier until they almost disappear like Tinkerbell (zzzzzz...)

I am beginning to use the hot keys more for inserting and managing the plots and equations and that saves a lot of time. It is really boring if I have to point and click all the time. Life is too short.

```
x <- seq(0, pi, len = 5)
y <- cbind(sin(x))
matplot(x, y, type = "b", xaxt = "n", cex=1 , pch=24,
main = expression(paste(plain(sin) * phi)),
ylab = expression("Trapezoidal approximation of sin" * phi),
xlab = expression(paste("x Phase ", phi)),
col.main = "blue")
axis(1, at = c(0, pi/4, pi/2,3*pi/4,pi),
labels = expression(0,Pi/4, Pi/2,3*Pi/4, Pi))
text(1.6, 0.4, expression(y==sinx))

```

OR

```
x = seq(0,pi,by=pi/4)
y = (sin(x))
plot(x,y,type='b' ,xaxt="n", pch=16)
text(01.5, 0.4, expression(y==sinx))
axis(1, at = c(0,pi/4, pi/2, 3*pi/4),
labels = expression(0, Pi/4,  Pi/2, 3*Pi/4))

```