What is the tangent of sin(3x) ?

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

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tangent of sin(3x)

tangent of

sin (3 x)

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

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

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

Find the slope of

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

Compute the slope of

y = sin (3 x)

x = a_{0} : m = cos (3 a_{0}) \cdot 3

Find the line with slope m=

cos (3 a_{0}) 3

and passing through

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

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

y = e^{x} + 1

\frac{d}{d x} (- 2 sin (2 x) + 2 cos (2 x))

\frac{x}{x - 8}

x \to 0 + lim (2 x e^{- 3 x})

\int_{0}^{16} \frac{500 x}{x ^{2} + 24} d x

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