How to draw the tangent to a curve passing through the origin

Hi,

I have the following code

xt = -1:0.1:1;
yt=-100-(2*(cos(xt)).^3)-(4*(cos(xt)).^2)-3*cos(xt);
plot(xt,yt)

and I get the blue curve as below. Now, I want to add a tangent line which must pass through the origin (as the black line I added "by hand" in the figure below).

I was thinking to use the function gradient but I am not sure how to impose the condition to pass through the (0,0).

Could you help me?

Answer 1

[Akira Agata]

Assuming that you want to obtain tangent lines which pass through the (-110,0), how about the following?

In this code, I changed delta xt from 0.1 to 0.01 in order to obtaion more accurate result.

xt = -1:0.01:1;
yt =-100-(2*(cos(xt)).^3)-(4*(cos(xt)).^2)-3*cos(xt);
dyt = gradient(yt,0.01);

% yt value of tangent line at xt = 0 for each point on the curve
ytValue = yt - xt.*dyt;

% Find the xt positions where ytValue is close to -110
[~,pt] = mink(abs(ytValue + 110),2);

% Tangent line
ytTangent1 = dyt(pt(1))*(xt - xt(pt(1))) + yt(pt(1));
ytTangent2 = dyt(pt(2))*(xt - xt(pt(2))) + yt(pt(2));

% Draw the curve and the tangent line
figure
plot(xt,yt)
hold on
plot(xt,ytTangent1)
plot(xt,ytTangent2)
grid on