What is the tangent of f(x)=3sin(x) ?

The tangent of f(x)=3sin(x) is y=3cos(a_{0})x+3sin(a_{0})-3cos(a_{0})a_{0}

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tangent of f(x)=3sin(x)

tangent of

f (x) = 3 sin (x)

y = 3 cos (a_{0}) x + 3 sin (a_{0}) - 3 cos (a_{0}) a_{0}

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

(a_{0}, 3 sin (a_{0}))

Find the slope of

f (x) = 3 sin (x) : \frac{df ( x )}{d x} = 3 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 = 3 cos (a_{0})

Find the line with slope m=

3 cos (a_{0})

and passing through

(a_{0}, 3 sin (a_{0})) : y = 3 cos (a_{0}) x + 3 sin (a_{0}) - 3 cos (a_{0}) a_{0}

y = 3 cos (a_{0}) x + 3 sin (a_{0}) - 3 cos (a_{0}) a_{0}

What is the tangent of f(x)=3sin(x) ?
The tangent of f(x)=3sin(x) is y=3cos(a_{0})x+3sin(a_{0})-3cos(a_{0})a_{0}