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人気のある三角関数 >

2cot(x)=csc(x)

解

2 cot (x) = csc (x)

解

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

+1

度

x = 6 0^{\circ} + 36 0^{\circ} n, x = 30 0^{\circ} + 36 0^{\circ} n

解答ステップ

2 cot (x) = csc (x)

両辺から

csc (x)

を引く

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

両辺に

1

を足す

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

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

グラフ

人気の例

-2sec^2(x)tan(x)=0

- 2 sec^{2} (x) tan (x) = 0

5tan^2(θ)-tan(θ)+12=8tan(θ)+8

5 tan^{2} (θ) - tan (θ) + 12 = 8 tan (θ) + 8

16sin^2(θ)-4=0

16 sin^{2} (θ) - 4 = 0

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

22 cos (x) - 2 = 0

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

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