What is the tangent of r=3cos(3θ) ?

The tangent of r=3cos(3θ) is r=-9sin(3a_{0})θ+3cos(3a_{0})+9a_{0}sin(3a_{0})

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tangent of r=3cos(3θ)

tangent of

r = 3 cos (3 θ)

r = - 9 sin (3 a_{0}) θ + 3 cos (3 a_{0}) + 9 a_{0} sin (3 a_{0})

Solution steps

Compute the tangent line to the general point

θ = a_{0}

Find the tangent point:

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

Find the slope of

r = 3 cos (3 θ) : \frac{d r}{d θ} = - 9 sin (3 θ)

Compute the slope of

r = 3 cos (3 θ)

θ = a_{0} : m = - 9 sin (3 a_{0})

Find the line with slope m=

- 9 sin (3 a_{0})

and passing through

(a_{0}, 3 cos (3 a_{0})) : r = - 9 sin (3 a_{0}) θ + 3 cos (3 a_{0}) + 9 a_{0} sin (3 a_{0})

r = - 9 sin (3 a_{0}) θ + 3 cos (3 a_{0}) + 9 a_{0} sin (3 a_{0})

\frac{\partial}{\partial y} (x^{2} y^{2} e^{2 x y})

x \to 1 lim (\frac{x ^{2}}{2})

\frac{d}{d x} (\frac{20 x}{x ^{2} - 5})

(x^{\frac{3}{2}})^{^{'}}

\frac{d}{d x} (\frac{3 x ^{2} - 3}{2 x})

What is the tangent of r=3cos(3θ) ?
The tangent of r=3cos(3θ) is r=-9sin(3a_{0})θ+3cos(3a_{0})+9a_{0}sin(3a_{0})