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人気のある微分積分 >

tangent (sin(t))/(2+2cos(t))

解

タンジェント

\frac{sin ( t )}{2 + 2 cos ( t )}

解

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

解答ステップ

一般的なポイントへの接線を計算する

t = a_{0}

接点を見つける:

(a_{0}, \frac{sin ( a _{0} )}{2 + 2 cos ( a _{0} )})

以下の傾斜を見つける:

y = \frac{sin ( t )}{2 + 2 cos ( t )} : \frac{d y}{d t} = \frac{cos ( t ) ( 2 + 2 cos ( t ) ) + 2 sin ^{2} ( t )}{( 2 + 2 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} ) ( 2 + 2 cos ( a _{0} ) ) + 2 sin ^{2} ( a _{0} )}{( 2 + 2 cos ( a _{0} ) ) ^{2}}

傾斜m=

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

で通過する線を見つける

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

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

グラフ

人気の例

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\frac{d}{d x} (\frac{d y}{d x}) - y = 0

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\int e^{4 x} sin (7 x) d x

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\int x^{2} cos (\frac{x}{9}) d x

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\int \frac{u ^{2}}{u ^{2} + 25} d u

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d er i v a t i v e \frac{3}{5} x^{10}