Find the slope of the tangent to the graph of the function y = sin x at the point with the abscissa x0 = n / 4
| September 19, 2021 | education
The slope of the tangent to the graph of the function f (x) at the point with the abscissa x0 is equal to the value of the derivative of this function at this point.
Therefore, to calculate the slope of the tangent to the graph of the function y = sinx at the point with the abscissa x0 = π / 4, it is necessary to calculate the value of the derivative of this function at the point x0 = π / 4.
Find the derivative of this function:
y ‘= (sinx)’ = cosx.
We calculate what the resulting derivative is equal to at the point x0 = π / 4:
y ‘(π / 4) = cos (π / 4) = √2 / 2.
Answer: the slope of the tangent to the graph of the function y = sinx at the point with the abscissa x0 = π / 4 is equal to √2 / 2.
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