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人気のある三角関数 >

cot(x)=cot(3x-50),0<x<180

解

cot (x) = cot (3 x - 5 0^{\circ}), 0 < x < 18 0^{\circ}

解

x = 2 5^{\circ}, x = 11 5^{\circ}

+1

ラジアン

x = \frac{5 π}{36}, x = \frac{23 π}{36}

解答ステップ

cot (x) = cot (3 x - 5 0^{\circ}), 0 < x < 18 0^{\circ}

両辺から

cot (3 x - 5 0^{\circ})

を引く

cot (x) - cot (3 x - 5 0^{\circ}) = 0

サイン, コサインで表わす

- cot (- 5 0^{\circ} + 3 x) + 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{cos ( - 5 0 ^{\circ} + 3 x )}{sin ( - 5 0 ^{\circ} + 3 x )} + 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{cos ( - 5 0 ^{\circ} + 3 x )}{sin ( - 5 0 ^{\circ} + 3 x )} + \frac{cos ( x )}{sin ( x )}

簡素化

- \frac{cos ( - 5 0 ^{\circ} + 3 x )}{sin ( - 5 0 ^{\circ} + 3 x )} + \frac{cos ( x )}{sin ( x )} : \frac{- cos ( \frac{- 90 0 ^{\circ} + 54 x}{18} ) sin ( x ) + cos ( x ) sin ( \frac{54 x - 90 0 ^{\circ}}{18} )}{sin ( \frac{54 x - 90 0 ^{\circ}}{18} ) sin ( x )}

- \frac{cos ( - 5 0 ^{\circ} + 3 x )}{sin ( - 5 0 ^{\circ} + 3 x )} + \frac{cos ( x )}{sin ( x )}

\frac{cos ( - 5 0 ^{\circ} + 3 x )}{sin ( - 5 0 ^{\circ} + 3 x )} = \frac{cos ( \frac{- 90 0 ^{\circ} + 54 x}{18} )}{sin ( \frac{- 90 0 ^{\circ} + 54 x}{18} )}

\frac{cos ( - 5 0 ^{\circ} + 3 x )}{sin ( - 5 0 ^{\circ} + 3 x )}

結合

- 5 0^{\circ} + 3 x : \frac{- 90 0 ^{\circ} + 54 x}{18}

- 5 0^{\circ} + 3 x

元を分数に変換する:

3 x = \frac{3 x 18}{18}

= - 5 0^{\circ} + \frac{3 x \cdot 18}{18}

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{- 90 0 ^{\circ} + 3 x \cdot 18}{18}

数を乗じる:

3 \cdot 18 = 54

= \frac{- 90 0 ^{\circ} + 54 x}{18}

= \frac{cos ( - 5 0 ^{\circ} + 3 x )}{sin ( \frac{- 90 0 ^{\circ} + 54 x}{18} )}

結合

- 5 0^{\circ} + 3 x : \frac{- 90 0 ^{\circ} + 54 x}{18}

- 5 0^{\circ} + 3 x

元を分数に変換する:

3 x = \frac{3 x 18}{18}

= - 5 0^{\circ} + \frac{3 x \cdot 18}{18}

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{- 90 0 ^{\circ} + 3 x \cdot 18}{18}

数を乗じる:

3 \cdot 18 = 54

= \frac{- 90 0 ^{\circ} + 54 x}{18}

= \frac{cos ( \frac{- 90 0 ^{\circ} + 54 x}{18} )}{sin ( \frac{- 90 0 ^{\circ} + 54 x}{18} )}

= - \frac{cos ( \frac{54 x - 90 0 ^{\circ}}{18} )}{sin ( \frac{54 x - 90 0 ^{\circ}}{18} )} + \frac{cos ( x )}{sin ( x )}

以下の最小公倍数:

sin (\frac{- 90 0 ^{\circ} + 54 x}{18}), sin (x) : sin (\frac{54 x - 90 0 ^{\circ}}{18}) sin (x)

sin (\frac{- 90 0 ^{\circ} + 54 x}{18}), sin (x)

最小公倍数 (LCM)

sin (\frac{- 90 0 ^{\circ} + 54 x}{18})

または以下のいずれかに現れる因数で構成された式を計算する:

sin (x)

= sin (\frac{54 x - 90 0 ^{\circ}}{18}) sin (x)

LCMに基づいて分数を調整する

該当する分母を乗じてLCMに変えるために

必要な量で各分子を乗じる

sin (\frac{54 x - 90 0 ^{\circ}}{18}) sin (x)

\frac{cos ( \frac{- 90 0 ^{\circ} + 54 x}{18} )}{sin ( \frac{- 90 0 ^{\circ} + 54 x}{18} )}

の場合

:

分母と分子に以下を乗じる:

sin (x)

\frac{cos ( \frac{- 90 0 ^{\circ} + 54 x}{18} )}{sin ( \frac{- 90 0 ^{\circ} + 54 x}{18} )} = \frac{cos ( \frac{- 90 0 ^{\circ} + 54 x}{18} ) sin ( x )}{sin ( \frac{- 90 0 ^{\circ} + 54 x}{18} ) sin ( x )}

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

の場合

:

分母と分子に以下を乗じる:

sin (\frac{54 x - 90 0 ^{\circ}}{18})

\frac{cos ( x )}{sin ( x )} = \frac{cos ( x ) sin ( \frac{54 x - 90 0 ^{\circ}}{18} )}{sin ( x ) sin ( \frac{54 x - 90 0 ^{\circ}}{18} )}

= - \frac{cos ( \frac{- 90 0 ^{\circ} + 54 x}{18} ) sin ( x )}{sin ( \frac{- 90 0 ^{\circ} + 54 x}{18} ) sin ( x )} + \frac{cos ( x ) sin ( \frac{54 x - 90 0 ^{\circ}}{18} )}{sin ( x ) sin ( \frac{54 x - 90 0 ^{\circ}}{18} )}

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 ( \frac{- 90 0 ^{\circ} + 54 x}{18} ) sin ( x ) + cos ( x ) sin ( \frac{54 x - 90 0 ^{\circ}}{18} )}{sin ( \frac{54 x - 90 0 ^{\circ}}{18} ) sin ( x )}

= \frac{- cos ( \frac{- 90 0 ^{\circ} + 54 x}{18} ) sin ( x ) + cos ( x ) sin ( \frac{54 x - 90 0 ^{\circ}}{18} )}{sin ( \frac{54 x - 90 0 ^{\circ}}{18} ) sin ( x )}

\frac{- cos ( \frac{54 x - 90 0 ^{\circ}}{18} ) sin ( x ) + cos ( x ) sin ( \frac{54 x - 90 0 ^{\circ}}{18} )}{sin ( \frac{54 x - 90 0 ^{\circ}}{18} ) sin ( x )} = 0

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

- cos (\frac{54 x - 90 0 ^{\circ}}{18}) sin (x) + cos (x) sin (\frac{54 x - 90 0 ^{\circ}}{18}) = 0

三角関数の公式を使用して書き換える

- cos (\frac{54 x - 90 0 ^{\circ}}{18}) sin (x) + cos (x) sin (\frac{54 x - 90 0 ^{\circ}}{18})

角の差の公式を使用する:

sin (s) cos (t) - cos (s) sin (t) = sin (s - t)

= sin (\frac{54 x - 90 0 ^{\circ}}{18} - x)

sin (\frac{54 x - 90 0 ^{\circ}}{18} - x) = 0

以下の一般解

sin (\frac{54 x - 90 0 ^{\circ}}{18} - x) = 0

sin (x)

36 0^{\circ} n

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}

\frac{54 x - 90 0 ^{\circ}}{18} - x = 0 + 36 0^{\circ} n, \frac{54 x - 90 0 ^{\circ}}{18} - x = 18 0^{\circ} + 36 0^{\circ} n

\frac{54 x - 90 0 ^{\circ}}{18} - x = 0 + 36 0^{\circ} n, \frac{54 x - 90 0 ^{\circ}}{18} - x = 18 0^{\circ} + 36 0^{\circ} n

解く

\frac{54 x - 90 0 ^{\circ}}{18} - x = 0 + 36 0^{\circ} n : x = 18 0^{\circ} n + 2 5^{\circ}

\frac{54 x - 90 0 ^{\circ}}{18} - x = 0 + 36 0^{\circ} n

0 + 36 0^{\circ} n = 36 0^{\circ} n

\frac{54 x - 90 0 ^{\circ}}{18} - x = 36 0^{\circ} n

以下で両辺を乗じる:

18

\frac{54 x - 90 0 ^{\circ}}{18} - x = 36 0^{\circ} n

以下で両辺を乗じる:

18

\frac{54 x - 90 0 ^{\circ}}{18} \cdot 18 - x \cdot 18 = 36 0^{\circ} n \cdot 18

簡素化

\frac{54 x - 90 0 ^{\circ}}{18} \cdot 18 - x \cdot 18 = 36 0^{\circ} n \cdot 18

簡素化

\frac{54 x - 90 0 ^{\circ}}{18} \cdot 18 : 54 x - 90 0^{\circ}

\frac{54 x - 90 0 ^{\circ}}{18} \cdot 18

分数を乗じる:

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

= \frac{( 54 x - 90 0 ^{\circ} ) \cdot 18}{18}

共通因数を約分する:

18

= 54 x - 90 0^{\circ}

簡素化

x \cdot 18 : 18 x

x \cdot 18

交換法則を適用する:

x \cdot 18 = 18 x

18 x

簡素化

36 0^{\circ} n \cdot 18 : 648 0^{\circ} n

36 0^{\circ} n \cdot 18

数を乗じる:

2 \cdot 18 = 36

= 648 0^{\circ} n

54 x - 90 0^{\circ} - 18 x = 648 0^{\circ} n

36 x - 90 0^{\circ} = 648 0^{\circ} n

36 x - 90 0^{\circ} = 648 0^{\circ} n

36 x - 90 0^{\circ} = 648 0^{\circ} n

90 0^{\circ}

を右側に移動します

36 x - 90 0^{\circ} = 648 0^{\circ} n

両辺に

90 0^{\circ}

を足す

36 x - 90 0^{\circ} + 90 0^{\circ} = 648 0^{\circ} n + 90 0^{\circ}

簡素化

36 x = 648 0^{\circ} n + 90 0^{\circ}

36 x = 648 0^{\circ} n + 90 0^{\circ}

以下で両辺を割る

36

36 x = 648 0^{\circ} n + 90 0^{\circ}

以下で両辺を割る

36

\frac{36 x}{36} = \frac{648 0 ^{\circ} n}{36} + 2 5^{\circ}

簡素化

x = 18 0^{\circ} n + 2 5^{\circ}

x = 18 0^{\circ} n + 2 5^{\circ}

解く

\frac{54 x - 90 0 ^{\circ}}{18} - x = 18 0^{\circ} + 36 0^{\circ} n : x = 11 5^{\circ} + 18 0^{\circ} n

\frac{54 x - 90 0 ^{\circ}}{18} - x = 18 0^{\circ} + 36 0^{\circ} n

以下で両辺を乗じる:

18

\frac{54 x - 90 0 ^{\circ}}{18} - x = 18 0^{\circ} + 36 0^{\circ} n

以下で両辺を乗じる:

18

\frac{54 x - 90 0 ^{\circ}}{18} \cdot 18 - x \cdot 18 = 18 0^{\circ} 18 + 36 0^{\circ} n \cdot 18

簡素化

\frac{54 x - 90 0 ^{\circ}}{18} \cdot 18 - x \cdot 18 = 18 0^{\circ} 18 + 36 0^{\circ} n \cdot 18

簡素化

\frac{54 x - 90 0 ^{\circ}}{18} \cdot 18 : 54 x - 90 0^{\circ}

\frac{54 x - 90 0 ^{\circ}}{18} \cdot 18

分数を乗じる:

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

= \frac{( 54 x - 90 0 ^{\circ} ) \cdot 18}{18}

共通因数を約分する:

18

= 54 x - 90 0^{\circ}

簡素化

x \cdot 18 : 18 x

x \cdot 18

交換法則を適用する:

x \cdot 18 = 18 x

18 x

簡素化

18 0^{\circ} 18 : 324 0^{\circ}

18 0^{\circ} 18

交換法則を適用する:

18 0^{\circ} 18 = 324 0^{\circ}

324 0^{\circ}

簡素化

36 0^{\circ} n \cdot 18 : 648 0^{\circ} n

36 0^{\circ} n \cdot 18

数を乗じる:

2 \cdot 18 = 36

= 648 0^{\circ} n

54 x - 90 0^{\circ} - 18 x = 324 0^{\circ} + 648 0^{\circ} n

36 x - 90 0^{\circ} = 324 0^{\circ} + 648 0^{\circ} n

36 x - 90 0^{\circ} = 324 0^{\circ} + 648 0^{\circ} n

36 x - 90 0^{\circ} = 324 0^{\circ} + 648 0^{\circ} n

90 0^{\circ}

を右側に移動します

36 x - 90 0^{\circ} = 324 0^{\circ} + 648 0^{\circ} n

両辺に

90 0^{\circ}

を足す

36 x - 90 0^{\circ} + 90 0^{\circ} = 324 0^{\circ} + 648 0^{\circ} n + 90 0^{\circ}

簡素化

36 x = 414 0^{\circ} + 648 0^{\circ} n

36 x = 414 0^{\circ} + 648 0^{\circ} n

以下で両辺を割る

36

36 x = 414 0^{\circ} + 648 0^{\circ} n

以下で両辺を割る

36

\frac{36 x}{36} = 11 5^{\circ} + \frac{648 0 ^{\circ} n}{36}

簡素化

x = 11 5^{\circ} + 18 0^{\circ} n

x = 11 5^{\circ} + 18 0^{\circ} n

x = 18 0^{\circ} n + 2 5^{\circ}, x = 11 5^{\circ} + 18 0^{\circ} n

範囲の解答

0 < x < 18 0^{\circ}

x = 2 5^{\circ}, x = 11 5^{\circ}

グラフ

人気の例

tan (2 θ) = \frac{4}{3}

cos(θ)-1=cos(2θ)

cos (θ) - 1 = cos (2 θ)

5tan(x)=9sin(x)

5 tan (x) = 9 sin (x)

sin (θ) = \frac{12}{37}

8tan(θ/2)+8cos(θ)tan(θ/2)=1

8 tan (\frac{θ}{2}) + 8 cos (θ) tan (\frac{θ}{2}) = 1