Find the angle between the tangent drawn to the graph of the function y = sin 2x – 0.5 at the point

Find the angle between the tangent drawn to the graph of the function y = sin 2x – 0.5 at the point with the abscissa equal to n / 3 and the positive ray of the abscissa axis.

We have a function:

y = sin 2x – 0.5.

The equation of the tangent to the graph of the function at the point with the abscissa x0 = P / 3 has the following form:

y = y ‘(x0) * (x – x0) + y (x0);

The tangent of the angle of inclination of the tangent to the graph of the function is equal to the coefficient of the variable, that is, y ‘(x0). Find the derivative:

y ‘(x) = 2 * cos 2x;

y ‘(x0) = 2 * cos (2 * P / 3) = 2 * (-1/2) = -1.

Accordingly, we find the angle that the tangent forms with the positive direction of the X axis:

A = arctan (-1) = 3 * P / 4.