How do you find an equation of the tangent line to the curve at the given point # y=sin(2x)# and #x=pi/2#?

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Answer 1 · 2017-12-17T15:46:20

See below.

First we need to differentiate #y=sin(2x)#. This will give us the gradient of the tangent line at the given point:

#d/dx(sin(2x))=cos(2x)*2=2cos(2x)#

Plugging in #x=pi/2#

#2cos(pi)=-2#

Equation Is:

#y-(0)=-2(x-pi/2)#

#y=-2x+pi#

Graph:

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