MATLAB: How to get 2 angle values for an asin

anglesasinmultiple

Hey guys, I'm trying to solve for 2 angles that have the same sine value.

i.e. if x = asin(0.5), then x could be 30 degrees or 150 degrees.

I can't get this to come out though.

tried declaring a 1×2 symbolic variable x: [x1,x2], but if I try:

S = solve('x = asin(0.5)',x)

Then what I get out is:

x = 0.52... (30 degrees)
x1 = 0
x2 = 0

Can anyone help me out here? What am I doing wrong?

Thanks,

Joshua

Best Answer

>> syms x
>> solve('0.5 = sin(x)',x)
ans =
   0.52359877559829887307710723054658
    2.6179938779914943653855361527329

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MATLAB: How to substitute a variable

So why not use subs? It works fine, as long as you use it as designed.

syms x
a = 5;
% I don't need the dot operators in a symbolic expression,
% but they do work too.
y = a*sin(x)^2 /(sin(x) + cos(x))
y =
(5*sin(x)^2)/(cos(x) + sin(x))
subs(y,x,1:pi/10:pi)
ans =
[ (5*sin(1)^2)/(cos(1) + sin(1)), (5*sin(739805897222023/562949953421312)^2)/(cos(739805897222023/562949953421312) + sin(739805897222023/562949953421312)), (5*sin(458330920511367/281474976710656)^2)/(cos(458330920511367/281474976710656) + sin(458330920511367/281474976710656)), (5*sin(1093517784823445/562949953421312)^2)/(cos(1093517784823445/562949953421312) + sin(1093517784823445/562949953421312)), (5*sin(317593432156039/140737488355328)^2)/(cos(317593432156039/140737488355328) + sin(317593432156039/140737488355328)), (5*sin(1447229672424867/562949953421312)^2)/(cos(1447229672424867/562949953421312) + sin(1447229672424867/562949953421312)), (5*sin(812042808112789/281474976710656)^2)/(cos(812042808112789/281474976710656) + sin(812042808112789/281474976710656))]

Not very easy to read that way, or that useful, so use vpa to improve things a bit...

vpa(subs(y,x,1:pi/10:pi))
ans =
[ 2.5621910014165363100864295707477, 3.8309204938871849945381706934322, 5.2967473394750604192098370433573, 7.6345151542111843907753899746208, 21.303646775422896588787558509401, -4.8465627759522670140582286462245, -0.45155218609854555823864593466888]

MATLAB: “asin” function is always solving between 0 and pi/2 of interval. Why

Most likelly because of the arguments you give it.

From the documentation:

For real values of X in the interval [-1, 1], asin(X) returns values in the interval [-π/2, π/2].

Illustrated here —

a=0.5;
x=[0.0  0.5 0.75 1.250  2.5 5.0 7.5 10  15  20  25  30  35  40  45  50  55  60  65  70  75  80  85  90  95  100]./100-0.5 ;
y=[0.0  0.394   0.475   0.594   0.795   1.090   1.322   1.518   1.828   2.066   2.245   2.375   2.459   2.498   2.487   2.420   2.290   2.106   1.881   1.623   1.339   1.038   0.729   0.430   0.165   0.0];
X=[x flip(x)]
X = 1×52
   -0.5000   -0.4950   -0.4925   -0.4875   -0.4750   -0.4500   -0.4250   -0.4000   -0.3500   -0.3000   -0.2500   -0.2000   -0.1500   -0.1000   -0.0500         0    0.0500    0.1000    0.1500    0.2000    0.2500    0.3000    0.3500    0.4000    0.4500    0.5000    0.5000    0.4500    0.4000    0.3500
Y=[y flip(y)]; 
for k=1:numel(X)
    p(k)       = 1-((X(k)./(2*a)).^2)-(Y(k)./(2*a)).^2;
    sin2the(k) = (p(k)+sqrt(p(k).^2+(Y(k)./a)^2));
    sinthe(k)  = sqrt(sin2the(k)./2);
    theta(k)   = asin(sinthe(k));
    psi(k)      = asinh(Y(k)./(2.*a.*sinthe(k)));
   
end
plot(theta,psi)
asinarg = [min(sinthe) max(sinthe)]
asinarg = 1×2
    0.8660    1.0000
asinv = asin(asinarg)
asinv = 1×2
    1.0472    1.5708
asinext = asin([-1 1])
asinext = 1×2
   -1.5708    1.5708

Best Answer

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MATLAB: How to substitute a variable

MATLAB: “asin” function is always solving between 0 and pi/2 of interval. Why

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