What is the tangent of (sin(t))/(4+4cos(t)) ?

The tangent of (sin(t))/(4+4cos(t)) is

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tangent of (sin(t))/(4+4cos(t))

tangent of

\frac{sin ( t )}{4 + 4 cos ( t )}

y = \frac{cos ( a _{0} ) ( 4 + 4 cos ( a _{0} ) ) + 4 sin ^{2} ( a _{0} )}{( 4 + 4 cos ( a _{0} ) ) ^{2}} t + \frac{4 ( sin ( a _{0} ) ( cos ( a _{0} ) + 1 ) - a _{0} ( sin ^{2} ( a _{0} ) + cos ( a _{0} ) ( cos ( a _{0} ) + 1 ) ) )}{( 4 + 4 cos ( a _{0} ) ) ^{2}}

Solution steps

Compute the tangent line to the general point

t = a_{0}

Find the tangent point:

(a_{0}, \frac{sin ( a _{0} )}{4 + 4 cos ( a _{0} )})

Find the slope of

y = \frac{sin ( t )}{4 + 4 cos ( t )} : \frac{d y}{d t} = \frac{cos ( t ) ( 4 + 4 cos ( t ) ) + 4 sin ^{2} ( t )}{( 4 + 4 cos ( t ) ) ^{2}}

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{cos ( a _{0} ) ( 4 + 4 cos ( a _{0} ) ) + 4 sin ^{2} ( a _{0} )}{( 4 + 4 cos ( a _{0} ) ) ^{2}}

Find the line with slope m=

\frac{cos ( a _{0} ) ( 4 + 4 cos ( a _{0} ) ) + 4 sin ^{2} ( a _{0} )}{( 4 + 4 cos ( a _{0} ) ) ^{2}}

and passing through

(a_{0}, \frac{sin ( a _{0} )}{4 + 4 cos ( a _{0} )}) : y = \frac{cos ( a _{0} ) ( 4 + 4 cos ( a _{0} ) ) + 4 sin ^{2} ( a _{0} )}{( 4 + 4 cos ( a _{0} ) ) ^{2}} t + \frac{4 ( sin ( a _{0} ) ( cos ( a _{0} ) + 1 ) - a _{0} ( sin ^{2} ( a _{0} ) + cos ( a _{0} ) ( cos ( a _{0} ) + 1 ) ) )}{( 4 + 4 cos ( a _{0} ) ) ^{2}}

y = \frac{cos ( a _{0} ) ( 4 + 4 cos ( a _{0} ) ) + 4 sin ^{2} ( a _{0} )}{( 4 + 4 cos ( a _{0} ) ) ^{2}} t + \frac{4 ( sin ( a _{0} ) ( cos ( a _{0} ) + 1 ) - a _{0} ( sin ^{2} ( a _{0} ) + cos ( a _{0} ) ( cos ( a _{0} ) + 1 ) ) )}{( 4 + 4 cos ( a _{0} ) ) ^{2}}

\int \frac{x ^{4}}{( 1 - x ^{2} ) ^{3}} d x

x^{2} ln (3 x)

\int x sin (x y) d y

x \to - 1 lim (2 x - 3)

x \to \infty lim ((1 + \frac{8}{x})^{\frac{x}{9}})

What is the tangent of (sin(t))/(4+4cos(t)) ?
The tangent of (sin(t))/(4+4cos(t)) is