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)

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 = \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}

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))