What is the equation of the tangent line

Jazmin Strong

Jazmin Strong

Answered question

2022-04-07

What is the equation of the tangent line of f(x)=cosxsinx at x=π3?

Answer & Explanation

o2z1zsjj0

o2z1zsjj0

Beginner2022-04-08Added 10 answers

f(π3)=cos(π3)sin(π3)=(12)(32)=34.
So the line we seek contains the point (π3,34).
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(2θ)=2sinθcosθ,
so f(x)=cosxsinx=12sin(2x)
And f(x)=cos(2x)
At x=π3 we get slope =cos(2π3)=12
The line through (π3,34), with slope m=12 is
y=12x+π6+34.

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