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#?

Answer 1

#y=-2x+pi/2#

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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Answer 2

The equation of the line tangent to the graph of y=cos(2x) at x=pi/4 is y = -sqrt(2)/2(x - pi/4) + sqrt(2)/2.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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