ja

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

人気のある三角関数 >

14sin(x+pi/2)+21tan(pi-x)=0

解

14 sin (x + \frac{π}{2}) + 21 tan (π - x) = 0

解

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

+1

度

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

解答ステップ

14 sin (x + \frac{π}{2}) + 21 tan (π - x) = 0

三角関数の公式を使用して書き換える

14 sin (x + \frac{π}{2}) + 21 tan (π - x) = 0

三角関数の公式を使用して書き換える

sin (x + \frac{π}{2})

角の和の公式を使用する:

sin (s + t) = sin (s) cos (t) + cos (s) sin (t)

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

簡素化

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

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

sin (x) cos (\frac{π}{2}) = 0

sin (x) cos (\frac{π}{2})

簡素化

cos (\frac{π}{2}) : 0

cos (\frac{π}{2})

次の自明恒等式を使用する:

cos (\frac{π}{2}) = 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}

= 0

= 0 \cdot sin (x)

規則を適用

0 \cdot a = 0

= 0

cos (x) sin (\frac{π}{2}) = cos (x)

cos (x) sin (\frac{π}{2})

簡素化

sin (\frac{π}{2}) : 1

sin (\frac{π}{2})

次の自明恒等式を使用する:

sin (\frac{π}{2}) = 1

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}

= 1

= 1 \cdot cos (x)

乗算:

cos (x) \cdot 1 = cos (x)

= cos (x)

= 0 + cos (x)

0 + cos (x) = cos (x)

= cos (x)

= cos (x)

基本的な三角関数の公式を使用する:

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

= \frac{sin ( π - x )}{cos ( π - x )}

角の差の公式を使用する:

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

= \frac{sin ( π ) cos ( x ) - cos ( π ) sin ( x )}{cos ( π - x )}

角の差の公式を使用する:

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

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

簡素化

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

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

sin (π) cos (x) - cos (π) sin (x) = sin (x)

sin (π) cos (x) - cos (π) sin (x)

sin (π) cos (x) = 0

sin (π) cos (x)

簡素化

sin (π) : 0

sin (π)

次の自明恒等式を使用する:

sin (π) = 0

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}

= 0

= 0 \cdot cos (x)

規則を適用

0 \cdot a = 0

= 0

cos (π) sin (x) = - sin (x)

cos (π) sin (x)

簡素化

cos (π) : - 1

cos (π)

次の自明恒等式を使用する:

cos (π) = (- 1)

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}

= - 1

= - 1 \cdot sin (x)

乗算:

1 \cdot sin (x) = sin (x)

= - sin (x)

= 0 - (- sin (x))

改良

= sin (x)

= \frac{sin ( x )}{cos ( π ) cos ( x ) + sin ( π ) sin ( x )}

cos (π) cos (x) + sin (π) sin (x) = - cos (x)

cos (π) cos (x) + sin (π) sin (x)

cos (π) cos (x) = - cos (x)

cos (π) cos (x)

簡素化

cos (π) : - 1

cos (π)

次の自明恒等式を使用する:

cos (π) = (- 1)

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}

= - 1

= - 1 \cdot cos (x)

乗算:

1 \cdot cos (x) = cos (x)

= - cos (x)

= - cos (x) + sin (π) sin (x)

sin (π) sin (x) = 0

sin (π) sin (x)

簡素化

sin (π) : 0

sin (π)

次の自明恒等式を使用する:

sin (π) = 0

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}

= 0

= 0 \cdot sin (x)

規則を適用

0 \cdot a = 0

= 0

= - cos (x) + 0

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

= - cos (x)

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

分数の規則を適用する:

\frac{a}{- b} = - \frac{a}{b}

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

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

14 cos (x) + 21 (- \frac{sin ( x )}{cos ( x )}) = 0

簡素化

14 cos (x) + 21 (- \frac{sin ( x )}{cos ( x )}) : 14 cos (x) - \frac{21 sin ( x )}{cos ( x )}

14 cos (x) + 21 (- \frac{sin ( x )}{cos ( x )})

括弧を削除する:

(- a) = - a

= 14 cos (x) - 21 \cdot \frac{sin ( x )}{cos ( x )}

乗じる

21 \cdot \frac{sin ( x )}{cos ( x )} : \frac{21 sin ( x )}{cos ( x )}

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

分数を乗じる:

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

= \frac{sin ( x ) \cdot 21}{cos ( x )}

= 14 cos (x) - \frac{21 sin ( x )}{cos ( x )}

14 cos (x) - \frac{21 sin ( x )}{cos ( x )} = 0

14 cos (x) - \frac{21 sin ( x )}{cos ( x )} = 0

簡素化

14 cos (x) - \frac{21 sin ( x )}{cos ( x )} : \frac{14 cos ^{2} ( x ) - 21 sin ( x )}{cos ( x )}

14 cos (x) - \frac{21 sin ( x )}{cos ( x )}

元を分数に変換する:

14 cos (x) = \frac{14 cos ( x ) cos ( x )}{cos ( x )}

= \frac{14 cos ( x ) cos ( x )}{cos ( x )} - \frac{21 sin ( x )}{cos ( 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{14 cos ( x ) cos ( x ) - 21 sin ( x )}{cos ( x )}

14 cos (x) cos (x) - 21 sin (x) = 14 cos^{2} (x) - 21 sin (x)

14 cos (x) cos (x) - 21 sin (x)

14 cos (x) cos (x) = 14 cos^{2} (x)

14 cos (x) cos (x)

指数の規則を適用する:

a^{b} \cdot a^{c} = a^{b + c}

cos (x) cos (x) = cos^{1 + 1} (x)

= 14 cos^{1 + 1} (x)

数を足す:

1 + 1 = 2

= 14 cos^{2} (x)

= 14 cos^{2} (x) - 21 sin (x)

= \frac{14 cos ^{2} ( x ) - 21 sin ( x )}{cos ( x )}

\frac{14 cos ^{2} ( x ) - 21 sin ( x )}{cos ( x )} = 0

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

14 cos^{2} (x) - 21 sin (x) = 0

三角関数の公式を使用して書き換える

14 cos^{2} (x) - 21 sin (x)

ピタゴラスの公式を使用する:

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

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

= 14 (1 - sin^{2} (x)) - 21 sin (x)

(1 - sin^{2} (x)) \cdot 14 - 21 sin (x) = 0

置換で解く

(1 - sin^{2} (x)) \cdot 14 - 21 sin (x) = 0

仮定:

sin (x) = u

(1 - u^{2}) \cdot 14 - 21 u = 0

(1 - u^{2}) \cdot 14 - 21 u = 0 : u = - 2, u = \frac{1}{2}

(1 - u^{2}) \cdot 14 - 21 u = 0

拡張

(1 - u^{2}) \cdot 14 - 21 u : 14 - 14 u^{2} - 21 u

(1 - u^{2}) \cdot 14 - 21 u

= 14 (1 - u^{2}) - 21 u

拡張

14 (1 - u^{2}) : 14 - 14 u^{2}

14 (1 - u^{2})

分配法則を適用する:

a (b - c) = ab - a c

a = 14, b = 1, c = u^{2}

= 14 \cdot 1 - 14 u^{2}

数を乗じる:

14 \cdot 1 = 14

= 14 - 14 u^{2}

= 14 - 14 u^{2} - 21 u

14 - 14 u^{2} - 21 u = 0

標準的な形式で書く

a x^{2} + b x + c = 0

- 14 u^{2} - 21 u + 14 = 0

解くとthe二次式

- 14 u^{2} - 21 u + 14 = 0

二次Equationの公式:

次の場合:

a = - 14, b = - 21, c = 14

u_{1, 2} = \frac{- ( - 21 ) \pm ( - 21 ) ^{2} - 4 ( - 14 ) \cdot 14}{2 ( - 14 )}

u_{1, 2} = \frac{- ( - 21 ) \pm ( - 21 ) ^{2} - 4 ( - 14 ) \cdot 14}{2 ( - 14 )}

(- 21)^{2} - 4 (- 14) \cdot 14 = 35

(- 21)^{2} - 4 (- 14) \cdot 14

規則を適用

- (- a) = a

= (- 21)^{2} + 4 \cdot 14 \cdot 14

指数の規則を適用する:

n

が偶数であれば

(- a)^{n} = a^{n}

(- 21)^{2} = 2 1^{2}

= 2 1^{2} + 4 \cdot 14 \cdot 14

数を乗じる:

4 \cdot 14 \cdot 14 = 784

= 2 1^{2} + 784

2 1^{2} = 441

= 441 + 784

数を足す:

441 + 784 = 1225

= 1225

数を因数に分解する:

1225 = 3 5^{2}

= 3 5^{2}

累乗根の規則を適用する:

n a^{n} = a

3 5^{2} = 35

= 35

u_{1, 2} = \frac{- ( - 21 ) \pm 35}{2 ( - 14 )}

解を分離する

u_{1} = \frac{- ( - 21 ) + 35}{2 ( - 14 )}, u_{2} = \frac{- ( - 21 ) - 35}{2 ( - 14 )}

u = \frac{- ( - 21 ) + 35}{2 ( - 14 )} : - 2

\frac{- ( - 21 ) + 35}{2 ( - 14 )}

括弧を削除する:

(- a) = - a, - (- a) = a

= \frac{21 + 35}{- 2 \cdot 14}

数を足す:

21 + 35 = 56

= \frac{56}{- 2 \cdot 14}

数を乗じる:

2 \cdot 14 = 28

= \frac{56}{- 28}

分数の規則を適用する:

\frac{a}{- b} = - \frac{a}{b}

= - \frac{56}{28}

数を割る:

\frac{56}{28} = 2

= - 2

u = \frac{- ( - 21 ) - 35}{2 ( - 14 )} : \frac{1}{2}

\frac{- ( - 21 ) - 35}{2 ( - 14 )}

括弧を削除する:

(- a) = - a, - (- a) = a

= \frac{21 - 35}{- 2 \cdot 14}

数を引く:

21 - 35 = - 14

= \frac{- 14}{- 2 \cdot 14}

数を乗じる:

2 \cdot 14 = 28

= \frac{- 14}{- 28}

分数の規則を適用する:

\frac{- a}{- b} = \frac{a}{b}

= \frac{14}{28}

共通因数を約分する:

14

= \frac{1}{2}

二次equationの解:

u = - 2, u = \frac{1}{2}

代用を戻す

u = sin (x)

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

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

sin (x) = - 2 :

解なし

sin (x) = - 2

- 1 \leq sin (x) \leq 1

解なし

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

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}{6} + 2 πn, x = \frac{5 π}{6} + 2 πn

グラフ

人気の例

8cos^3(x)=8cos(x)

8 cos^{3} (x) = 8 cos (x)

4cos(2θ)=cos^2(θ)-2

4 cos (2 θ) = cos^{2} (θ) - 2

2cos^2(x)+sin(x)=1,0<= x<= 2pi

2 cos^{2} (x) + sin (x) = 1, 0 \leq x \leq 2 π

cos(x)=(sqrt(5))/5

cos (x) = \frac{5}{5}

(sec(t)-2)(cot(t)+1)=0

(sec (t) - 2) (cot (t) + 1) = 0