What is the tangent of cos(3x) ?

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

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tangent of cos(3x)

tangent of

cos (3 x)

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

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

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

Find the slope of

y = cos (3 x) : \frac{d y}{d x} = - sin (3 x) \cdot 3

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 = - sin (3 a_{0}) \cdot 3

Find the line with slope m=

- sin (3 a_{0}) 3

and passing through

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

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

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