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人気のある三角関数 >

2cot(x)+csc(x)=0

解

2 cot (x) + csc (x) = 0

解

x = \frac{2 π}{3} + 2 πn, x = \frac{4 π}{3} + 2 πn

+1

度

x = 12 0^{\circ} + 36 0^{\circ} n, x = 24 0^{\circ} + 36 0^{\circ} n

解答ステップ

2 cot (x) + csc (x) = 0

サイン, コサインで表わす

csc (x) + 2 cot (x)

基本的な三角関数の公式を使用する:

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

= \frac{1}{sin ( x )} + 2 cot (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{1}{sin ( x )} + 2 \cdot \frac{cos ( x )}{sin ( x )}

簡素化

\frac{1}{sin ( x )} + 2 \cdot \frac{cos ( x )}{sin ( x )} : \frac{1 + 2 cos ( x )}{sin ( x )}

\frac{1}{sin ( x )} + 2 \cdot \frac{cos ( x )}{sin ( x )}

乗じる

2 \cdot \frac{cos ( x )}{sin ( x )} : \frac{2 cos ( x )}{sin ( x )}

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

分数を乗じる:

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

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

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

規則を適用

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

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

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

\frac{1 + 2 cos ( x )}{sin ( x )} = 0

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

1 + 2 cos (x) = 0

1

を右側に移動します

1 + 2 cos (x) = 0

両辺から

1

を引く

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

簡素化

2 cos (x) = - 1

2 cos (x) = - 1

以下で両辺を割る

2

2 cos (x) = - 1

以下で両辺を割る

2

\frac{2 cos ( x )}{2} = \frac{- 1}{2}

簡素化

cos (x) = - \frac{1}{2}

cos (x) = - \frac{1}{2}

以下の一般解

cos (x) = - \frac{1}{2}

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{2 π}{3} + 2 πn, x = \frac{4 π}{3} + 2 πn

x = \frac{2 π}{3} + 2 πn, x = \frac{4 π}{3} + 2 πn

グラフ

人気の例

sin (x) = - 0.15

74=58cos(x)+71sin(x)

74 = 58 cos (x) + 71 sin (x)

5 sin (x) + 4 = 0

tan (θ) = - \frac{7}{24}

2sin(2θ)=-sqrt(3)

2 sin (2 θ) = - 3