How do you find the equation of the line tangent to the graph of #y = sin(x) # at the point x=pi?
1 Answer
Sep 5, 2015
y = - x + pi
Explanation:
We differentiate the function sin x to get cos x.
The derivative of any function represents the slope or gradient of the tangent line t tat function at any point x.
Therefore, in particular at the point x = pi, we substitute pi into the derivative to get a slope of - 1.
Since a tangent is a straight line graph, it has equation y = mx + c, with m gradient and c the y-intercept.
We then substitute a point on the graph (the tangent contact point) into this equation to solve for the y-intercept value c, and rewrite in standard form.
Details in sketch below.
