What is the tangent of y=3sin(x),\at x= pi/6 ?

The tangent of y=3sin(x),\at x= pi/6 is y=(3sqrt(3))/2 x+3/2-(sqrt(3)pi)/4

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tangent of y=3sin(x),\at x= pi/6

tangent of

y = 3 sin (x), at x = \frac{π}{6}

y = \frac{3 3}{2} x + \frac{3}{2} - \frac{3 π}{4}

Solution steps

Find the tangent point:

(\frac{π}{6}, \frac{3}{2})

Find the slope of

y = 3 sin (x) : \frac{d y}{d x} = 3 cos (x)

Compute the slope of

y = 3 sin (x)

x = \frac{π}{6} : m = \frac{3 3}{2}

Find the line with slope m=

\frac{3 3}{2}

and passing through

(\frac{π}{6}, \frac{3}{2}) : y = \frac{3 3}{2} x + \frac{3}{2} - \frac{3 π}{4}

y = \frac{3 3}{2} x + \frac{3}{2} - \frac{3 π}{4}

\frac{d y}{d x}, e^{x} y = 2

\int (2 x + 5 - \frac{1}{x}) d x

\frac{\partial}{\partial y} (6 x y)

\int \frac{y}{( x ^{2} + y ^{2} )} d y

\frac{d}{d x} (\frac{x ^{3} - 2}{x})

What is the tangent of y=3sin(x),\at x= pi/6 ?
The tangent of y=3sin(x),\at x= pi/6 is y=(3sqrt(3))/2 x+3/2-(sqrt(3)pi)/4