Find the equation of the tangent line to the curve y=2sin(x) when x=π/3?

1 Answer
VNVDVI
Mar 1, 2018

#y=x-pi/3+sqrt(3)#

Explanation:

Take the first derivative:

#y'=2cos(x)#

Recall that the derivative of a function, graphically interpreted, tells us the slope of the curve of the function at a certain point #x#. So, the slope of the tangent line at #x=pi/3# can be obtained by plugging in #x=pi/3# into #y':#

#y'(pi/3)=2cos(pi/3)=cancel2(1/cancel2)=1#

The slope of the tangent line at #x=pi/3# is #1.# To find the full equation, use the point-slope form of a line:

#y-y_1=m(x-x_1)# where #(x_1,y_1)# is a point on the curve and #m# is the slope.

We have #x_1=pi/3,# thus #y_1=2sin(pi/3)=(2sqrt(3)/2)=sqrt(3)#

#(x_1,y_1)=(pi/3,sqrt(3)), m=1#

Plugging in, we get:

#y-sqrt(3)=1(x-pi/3)#

#y-sqrt(3)=x-pi/3#

#y=x-pi/3+sqrt(3)#

Related questions
Impact of this question
7642 views around the world
You can reuse this answer
Creative Commons License