Write the equation of the tangent to the graph f (x) = 1 + cosx at the point Xо = (- P / 2)

We have a function:

y = 1 + cos x.

The equation of the tangent to the graph of the function at the point with the abscissa x0 has the form:

y = y ‘(x0) * (x – x0) + y (x0);

Step by step we find the value of the function and its derivative at the point with the abscissa x0:

y (x0) = 1 + cos (-П / 2) = 1 + 0 = 1;

y ‘(x) = 1 – sin x;

y ‘(x0) = 1 – sin (-П / 2) = 1 + sin (П / 2) = 1 + 1 = 2;

Substitute the obtained values into the tangent formula:

y = 2 * (x + п / 2) + 1;

y = 2 * x + п + 1;

y = 2 * x + 4.14 is the equation of the tangent to the graph of the function at this point.