How do you find the equation of the tangent line to the graph of #y = sin(x)# at #x = pi#?

1 Answer
Apr 9, 2015

First evaluate the derivative of your function and evaluate it in your point with #x=pi# to find the slope of the tangent line:
#y'=cos(x)#
in #x=pi#
#y'(pi)=cos(pi)=-1#

Second find the point where your tangent touches your curve. You know that #x=pi# and substituting into your original function you'll get the corresponding value of y which is #y=sin(pi)=0#.
So, the tangent line has slope #m=-1# and passes through (#x_0=pi,y_0=0#);
the equation can be found using:
#y-y_0=m(x-x_0)#
or
#y-0=-1(x-pi)#
#y=-x+pi#

Graphically:
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