What is the tangent of y=7cos(x),\at x= pi/3 ?

The tangent of y=7cos(x),\at x= pi/3 is y=-(7sqrt(3))/2 x+7/2+(7pi)/(2sqrt(3))

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tangent of y=7cos(x),\at x= pi/3

tangent of

y = 7 cos (x), at x = \frac{π}{3}

y = - \frac{7 3}{2} x + \frac{7}{2} + \frac{7 π}{2 3}

Solution steps

Find the tangent point:

(\frac{π}{3}, \frac{7}{2})

Find the slope of

y = 7 cos (x) : \frac{d y}{d x} = - 7 sin (x)

Compute the slope of

y = 7 cos (x)

x = \frac{π}{3} : m = - \frac{7 3}{2}

Find the line with slope m=

- \frac{7 3}{2}

and passing through

(\frac{π}{3}, \frac{7}{2}) : y = - \frac{7 3}{2} x + \frac{7}{2} + \frac{7 π}{2 3}

y = - \frac{7 3}{2} x + \frac{7}{2} + \frac{7 π}{2 3}

y^{^{'}} = 0.4 (10 - x) (5 - x)

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What is the tangent of y=7cos(x),\at x= pi/3 ?
The tangent of y=7cos(x),\at x= pi/3 is y=-(7sqrt(3))/2 x+7/2+(7pi)/(2sqrt(3))