Home > Calculus > Tangent Line to a Curve

What is the equation of the tangent line of #f(x)=cosxsinx # at #x=pi/3#?

Answer 1

#y=-1/2x+pi/6+sqrt3/4#

#f(pi/3) = cos(pi/3)sin(pi/3) = (1/2)(sqrt3/2) = sqrt3/4#.

So the line we seek contains the point #(pi/3, sqrt3/4)#.

The slope is given by the derivative. We could differentiate by using the chain rule, but let's use some trigonometry to rewrite the function instead.

#sin(2theta) = 2sinthetacostheta#,

so #f(x) = cosxsinx=1/2sin(2x)#

And #f'(x) = cos(2x)#.

At #x=pi/3# we get slope = #cos((2pi)/3)= -1/2#

The line through #(pi/3, sqrt3/4)#, with slope #m= -1/2# is

#y=-1/2x+pi/6+sqrt3/4#.

By signing up, you agree to our Terms of Service and Privacy Policy

Answer 2

Emma Aldridge

The equation of the tangent line of f(x)=cosxsinx at x=pi/3 is y = sqrt(3)/4 * x + sqrt(3)/8.

By signing up, you agree to our Terms of Service and Privacy Policy

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.