What is the tangent of f(x)=6sin(x),\at x= pi/6 ?

The tangent of f(x)=6sin(x),\at x= pi/6 is y=3sqrt(3)x+3-(sqrt(3)pi)/2

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tangent of f(x)=6sin(x),\at x= pi/6

tangent of

f (x) = 6 sin (x), at x = \frac{π}{6}

y = 33 x + 3 - \frac{3 π}{2}

Solution steps

Find the tangent point:

(\frac{π}{6}, 3)

Find the slope of

f (x) = 6 sin (x) : \frac{df ( x )}{d x} = 6 cos (x)

EN : T i tl e G e n er a l Eq u a t i o n Sl o p e A t P o in t 2 Eq : m = 33

Find the line with slope m=

33

and passing through

(\frac{π}{6}, 3) : y = 33 x + 3 - \frac{3 π}{2}

y = 33 x + 3 - \frac{3 π}{2}

What is the tangent of f(x)=6sin(x),\at x= pi/6 ?
The tangent of f(x)=6sin(x),\at x= pi/6 is y=3sqrt(3)x+3-(sqrt(3)pi)/2