why is not equal

sigma_0 = 2;

theta_deg = [0, 90, 180, 270];

theta_rad = deg2rad(theta_deg);

r = 1:0.1:2;

shear_Q = zeros(length(r), length(theta_rad));

for i = 1:length(theta_rad)

theta = theta_rad(i);

ksi = 1./r;

shear_Q(:, i) = (-1/2.*sigma_0.*(1-(3.*(ksi.^4))+(2.*(ksi.^2))).*sin(2.*theta));

end

Why doesn't it give the same result for 0 and 180 degrees? or 90 and 270 . The result must be 0 for 0 and 180 degrees

[Rena Berman]

(Answers Dev) Restored edit

Answer 1

[Steven Lord]

Rather than converting from degrees to radians and then computing the sine of the angle in radians, why not just use the sind function?

sigma_0 = 2;
theta_deg = [0, 90, 180, 270]; 
r = 1:0.1:2;
shear_Q = zeros(length(r), length(theta_deg));
shear_Q_rad = shear_Q;
for i = 1:length(theta_deg)
       theta = theta_deg(i);
       thetaR = deg2rad(theta);
       ksi = 1./r;
       shear_Q(:, i) = (-1/2.*sigma_0.*(1-(3.*(ksi.^4))+(2.*(ksi.^2))).*sind(2.*theta));
       shear_Q_rad(:, i) = (-1/2.*sigma_0.*(1-(3.*(ksi.^4))+(2.*(ksi.^2))).*sin(2.*thetaR));
end
shear_Q

shear_Q = 11x4

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

Of course, 2 times each of the angles in theta_deg makes the angle a multiple of 180 degrees, and the sine of an integer multiple of 180 degrees gives us 0.

shear_Q_rad

shear_Q_rad = 11x4

1.0e-15 * 0 0 0 0 0 -0.0740 0.1479 -0.2219 0 -0.1154 0.2308 -0.3461 0 -0.1388 0.2775 -0.4163 0 -0.1518 0.3036 -0.4554 0 -0.1588 0.3175 -0.4763 0 -0.1621 0.3242 -0.4862 0 -0.1632 0.3265 -0.4897 0 -0.1631 0.3261 -0.4892 0 -0.1621 0.3242 -0.4864

Now why are the elements of shear_Q_rad not all zero? Go ahead and type out the exact transcendental value of the constant π. Go ahead, I'll wait for you to get to the last digit. Roundoff error creeps in when you convert the angle in degrees into the angle in radians.

Alternately, you may find the sinpi function useful.