How to plot general solution of a trigonometric function???

I want to plot a graph of a and b defined by this equation. 1-2*cosd(a)+2*cosd(b)=0 when I started plotting only graph of the principal solutions of cos is considered. whereas i want all possibilities of general solutions. by using contour only plot of functions can be drawn. what do i do now????

[HARSHA GYANANI]

x=0:1:90
y=(acosd((-1+2*cosd(5*x))/2))/5;
plot(x,y)

this is coming as

but i want this to be as

how can it be done???

[Walter Roberson]

The straight line is not present in the plot unless you ignore the imaginary component of y.

What would be the equation for the other parts you want drawn? Those curves are not the half circles.

[HARSHA GYANANI]

equation is same as matlab only follows principal solution but i want graphs for general solution. when i manually plotted by considering all the solution that comes out to be as 2nd graph.for eg. acosd(0)=90,270 and so on i want to get all possibiliities

[Walter Roberson]

Why stop at two solutions? Why not also look at 450, 630, and so on?

[HARSHA GYANANI]

I want to look at more but when problem occured i had to stop. Please do help me in this...

[Walter Roberson]

The below code requires R2016b or later:

Macosd = @(X) sort([(-1800:360:1800).'+acosd(X); (-1800:360:1800).'-acosd(X)]);
x = linspace(0, 90, 361);
y = (Macosd((-1+2*cosd(5*x))/2))./5;
plot(x, real(y))

If you zoom into the region near x = 24, you might see what looks like a "bounce". This is a side effect of the fact that when you start talking about taking multiple non-principle branches of the acosd, that the ordering of the branches is not well defined. Also, the sorting is not well defined for the places where acosd is imaginary. Also, as a limitation, the Macosd function produces duplicate points for cosd = +/- 1, but that case cannot show up in this particular use of it.

For release before R2016b, the code could be rewritten to use bsxfun.

[HARSHA GYANANI]

I am using 2015,,,, can u please send me code of 2015a as i dont know how to convert this using bsxfun

[Walter Roberson]

Macosd = @(X) sort([ bsxfun(@plus, (-1800:360:1800).', acosd(X));  bsxfun(@minus, (-1800:360:1800).', acosd(X))]);

Answer 1

[KSSV]

N = 100 ;
a = linspace(0,2*pi,N) ;
b = linspace(0,2*pi,N) ;
[X,Y] = meshgrid(a,b) ;
Z = 1-2*cos(X)+2*cos(Y) ;
surf(X,Y,Z)
hold on
contour(X,Y,Z,[0 0],'r')

[HARSHA GYANANI]

Thanku sir, but i want a 2D plot on X and Y axis.

[KSSV]

contour(X,Y,Z,[0 0],'r')

[HARSHA GYANANI]

this command is giving a 3D plot.

[Vivek Kumar]

bro please help me to plot a graph delta_lambda=h(1-cosX)/cm please help me

[Walter Roberson]

Vivek Kumar: you should open a new Question for that. In that Question, please indicate which variables are your independent variables, and what range of values you want, and what style of plot you want.

Answer 2

[Torsten]

Derive b as a function of a, prescribe a range for a, calculate b and use "plot(a,b)".

Best wishes

Torsten.