What is an equation of the line tangent to the graph of #y=cos(2x)# at #x=pi/4#?

What is an equation of the line tangent to the graph of #y=cos(2x)# at #x=pi/4#?

What is an equation of the line tangent to the graph of #y=cos(2x)# at #x=pi/4#?

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5
Dec 20, 2016

Answer:

#y=-2x+pi/2#

Explanation:

To find the equation of the tangent line to the curve #y=cos(2x)# at #x=pi/4#, start by taking the derivative of #y# (use the chain rule).

#y'=-2sin(2x)#

Now plug in your value for #x# into #y'#:

#-2sin(2*pi/4)=-2#

This is the slope of the tangent line at #x=pi/4#.

To find the equation of the tangent line, we need a value for #y#. Simply plug your #x# value into the original equation for #y#.

#y=cos(2*pi/4)#
#y=0#

Now use point slope form to find the equation of the tangent line:

#y-y_0=m(x-x_0)#

Where #y_0=0#, #m=-2# and #x_0=pi/4#.

This gives us:

#y=-2(x-pi/4)#

Simplifying,

#y=-2x+pi/2#

Hope that helps!
graph{(y-cos(2x))(y+2x-pi/2)=0 [-2.5, 2.5, -1.25, 1.25]}

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