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人気のある三角関数 >

2cos(x)=cot(x)

解

2 cos (x) = cot (x)

解

x = \frac{π}{2} + 2 πn, x = \frac{3 π}{2} + 2 πn, x = \frac{π}{6} + 2 πn, x = \frac{5 π}{6} + 2 πn

+1

度

x = 9 0^{\circ} + 36 0^{\circ} n, x = 27 0^{\circ} + 36 0^{\circ} n, x = 3 0^{\circ} + 36 0^{\circ} n, x = 15 0^{\circ} + 36 0^{\circ} n

解答ステップ

2 cos (x) = cot (x)

両辺から

cot (x)

を引く

2 cos (x) - cot (x) = 0

サイン, コサインで表わす

- cot (x) + 2 cos (x)

基本的な三角関数の公式を使用する:

cot (x) = \frac{cos ( x )}{sin ( x )}

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

簡素化

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

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

元を分数に変換する:

2 cos (x) = \frac{2 cos ( x ) sin ( x )}{sin ( x )}

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

分母が等しいので, 分数を組み合わせる:

\frac{a}{c} \pm \frac{b}{c} = \frac{a \pm b}{c}

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

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

\frac{- cos ( x ) + 2 cos ( x ) sin ( x )}{sin ( x )} = 0

\frac{f ( x )}{g ( x )} = 0 \Rightarrow f (x) = 0

- cos (x) + 2 cos (x) sin (x) = 0

因数

- cos (x) + 2 cos (x) sin (x) : cos (x) (2 sin (x) - 1)

- cos (x) + 2 cos (x) sin (x)

共通項をくくり出す

cos (x)

= cos (x) (- 1 + 2 sin (x))

cos (x) (2 sin (x) - 1) = 0

各部分を別個に解く

cos (x) = 0 or 2 sin (x) - 1 = 0

cos (x) = 0 : x = \frac{π}{2} + 2 πn, x = \frac{3 π}{2} + 2 πn

cos (x) = 0

以下の一般解

cos (x) = 0

cos (x)

2 πn

循環を含む周期性テーブル:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} cos (x) 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} cos (x) - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2}

x = \frac{π}{2} + 2 πn, x = \frac{3 π}{2} + 2 πn

x = \frac{π}{2} + 2 πn, x = \frac{3 π}{2} + 2 πn

2 sin (x) - 1 = 0 : x = \frac{π}{6} + 2 πn, x = \frac{5 π}{6} + 2 πn

2 sin (x) - 1 = 0

1

を右側に移動します

2 sin (x) - 1 = 0

両辺に

1

を足す

2 sin (x) - 1 + 1 = 0 + 1

簡素化

2 sin (x) = 1

2 sin (x) = 1

以下で両辺を割る

2

2 sin (x) = 1

以下で両辺を割る

2

\frac{2 sin ( x )}{2} = \frac{1}{2}

簡素化

sin (x) = \frac{1}{2}

sin (x) = \frac{1}{2}

以下の一般解

sin (x) = \frac{1}{2}

sin (x)

2 πn

循環を含む周期性テーブル:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} sin (x) 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2}

x = \frac{π}{6} + 2 πn, x = \frac{5 π}{6} + 2 πn

x = \frac{π}{6} + 2 πn, x = \frac{5 π}{6} + 2 πn

すべての解を組み合わせる

x = \frac{π}{2} + 2 πn, x = \frac{3 π}{2} + 2 πn, x = \frac{π}{6} + 2 πn, x = \frac{5 π}{6} + 2 πn

グラフ

人気の例

sqrt(3)cos(x)+sin(x)=2

3 cos (x) + sin (x) = 2

cos(2t)-cos(t)=-0.5

cos (2 t) - cos (t) = - 0.5

sin^2(x)-cos(x)+1=0

sin^{2} (x) - cos (x) + 1 = 0

tan(2x)=2sin(x)

tan (2 x) = 2 sin (x)

sin(θ)-cos(θ)=sqrt((2+\sqrt{3))/2}

sin (θ) - cos (θ) = \frac{2 + 3}{2}