What is the tangent of f(x)=5sec(x),\at x= pi/6 ?

The tangent of f(x)=5sec(x),\at x= pi/6 is y= 10/3 x+(10}{sqrt(3)}-\frac{5pi)/9

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tangent of f(x)=5sec(x),\at x= pi/6

tangent of

f (x) = 5 sec (x), at x = \frac{π}{6}

y = \frac{10}{3} x + \frac{10}{3} - \frac{5 π}{9}

Solution steps

Find the tangent point:

(\frac{π}{6}, \frac{10}{3})

Find the slope of

f (x) = 5 sec (x) : \frac{df ( x )}{d x} = 5 sec (x) tan (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{10}{3}

Find the line with slope m=

\frac{10}{3}

and passing through

(\frac{π}{6}, \frac{10}{3}) : y = \frac{10}{3} x + \frac{10}{3} - \frac{5 π}{9}

y = \frac{10}{3} x + \frac{10}{3} - \frac{5 π}{9}

What is the tangent of f(x)=5sec(x),\at x= pi/6 ?
The tangent of f(x)=5sec(x),\at x= pi/6 is y= 10/3 x+(10}{sqrt(3)}-\frac{5pi)/9