What is the tangent of f(x)=-5sin(x),\at x= pi/4 ?

The tangent of f(x)=-5sin(x),\at x= pi/4 is y=-5/(sqrt(2))x-5/(sqrt(2))+(5pi)/(4sqrt(2))

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tangent of f(x)=-5sin(x),\at x= pi/4

tangent of

f (x) = - 5 sin (x), at x = \frac{π}{4}

y = - \frac{5}{2} x - \frac{5}{2} + \frac{5 π}{4 2}

Solution steps

Find the tangent point:

(\frac{π}{4}, - \frac{5}{2})

Find the slope of

f (x) = - 5 sin (x) : \frac{df ( x )}{d x} = - 5 cos (x)

Compute the slope of

f (x) = - 5 sin (x)

x = \frac{π}{4} : m = - \frac{5}{2}

Find the line with slope m=

- \frac{5}{2}

and passing through

(\frac{π}{4}, - \frac{5}{2}) : y = - \frac{5}{2} x - \frac{5}{2} + \frac{5 π}{4 2}

y = - \frac{5}{2} x - \frac{5}{2} + \frac{5 π}{4 2}

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What is the tangent of f(x)=-5sin(x),\at x= pi/4 ?
The tangent of f(x)=-5sin(x),\at x= pi/4 is y=-5/(sqrt(2))x-5/(sqrt(2))+(5pi)/(4sqrt(2))