Angieda4msshatt Angieda4msshatt

24-11-2016
Mathematics

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Find an equation of the tangent line to the graph of the function f(x) = 2sinx at the point where x = pi/3.

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nobillionaireNobley nobillionaireNobley

25-11-2016

The equation of the tangent line of f(x) is given by y = f'(x)x + c
f(x) = 2sin x
f'(x) = 2cos x

At x = pi/3
f'(pi/3) = 2 cos(pi/3) = 1
f(pi/3) = 2 sin(pi/3) = √3
√3 = 1(π/3) + c
c = √3 - π/3

Therefore, required equation is
y = x + √3 - π/3

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