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"asin" function is always solving between 0 and pi/2 of interval. Why?

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I am encounering a problem when using asin function. function is solving the problem always between 0 and pi/2. why?
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)]
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)
graphic of psi againts theta must be like in picture

Accepted Answer

Star Strider
Star Strider on 31 May 2021
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
.
  6 Comments
Star Strider
Star Strider on 31 May 2021
@Torsten Thank you!
I am now confused. I have no idea what the actual problem is.

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