secd vs sec

x=-89.5:0.001:89.5; y=1./secd(x); trapz(x,y) Gives 114

AND

x=-pi/2:0.001:pi/2; y=1./sec(x); trapz(x,y) Gives 2

Why?

Answer 1

[Geoff]

Because your data ranges are different.

The area underneath the curve spanning -89.5:0.001:89.5 is approximately 180/pi times larger than the area underneath the curve spanning -pi/2:0.001:pi/2.

Your answers are correct, except you are using two different ranges. Surely the comparable range in degrees is -90:0.001:90

Note also that the step size for your degrees makes that calculation much more accurate than your radians range (which is using the same step size).

[edit] Compare apples with apples...

xd = -90:0.001:90;
yd = 1./secd(xd);
xr = xd * pi / 180;
yr = 1./sec(xr); 

% Use radians for x-axis in both calculations
zd = trapz(xr, yd)
zr = trapz(xr, yr)