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 >

5sin^2(x)cos(7x)-cos(7x)=0

解

5 sin^{2} (x) cos (7 x) - cos (7 x) = 0

解

x = \frac{π}{14} + \frac{2 πn}{7}, x = \frac{3 π}{14} + \frac{2 πn}{7}, x = - 0.46364 \dots + 2 πn, x = π + 0.46364 \dots + 2 πn, x = 0.46364 \dots + 2 πn, x = π - 0.46364 \dots + 2 πn

+1

度

x = 12.85714 \dots^{\circ} + 51.42857 \dots^{\circ} n, x = 38.57142 \dots^{\circ} + 51.42857 \dots^{\circ} n, x = - 26.56505 \dots^{\circ} + 36 0^{\circ} n, x = 206.56505 \dots^{\circ} + 36 0^{\circ} n, x = 26.56505 \dots^{\circ} + 36 0^{\circ} n, x = 153.43494 \dots^{\circ} + 36 0^{\circ} n

解答ステップ

5 sin^{2} (x) cos (7 x) - cos (7 x) = 0

因数

5 sin^{2} (x) cos (7 x) - cos (7 x) : cos (7 x) (5 sin (x) + 1) (5 sin (x) - 1)

5 sin^{2} (x) cos (7 x) - cos (7 x)

共通項をくくり出す

cos (7 x)

= cos (7 x) (5 sin^{2} (x) - 1)

因数

5 sin^{2} (x) - 1 : (5 sin (x) + 1) (5 sin (x) - 1)

5 sin^{2} (x) - 1

5 sin^{2} (x) - 1

を書き換え

(5 sin (x))^{2} - 1^{2}

5 sin^{2} (x) - 1

累乗根の規則を適用する:

a = (a)^{2}

5 = (5)^{2}

= (5)^{2} sin^{2} (x) - 1

1

を書き換え

1^{2}

= (5)^{2} sin^{2} (x) - 1^{2}

指数の規則を適用する:

a^{m} b^{m} = (ab)^{m}

(5)^{2} sin^{2} (x) = (5 sin (x))^{2}

= (5 sin (x))^{2} - 1^{2}

= (5 sin (x))^{2} - 1^{2}

2乗の差の公式を適用する:

x^{2} - y^{2} = (x + y) (x - y)

(5 sin (x))^{2} - 1^{2} = (5 sin (x) + 1) (5 sin (x) - 1)

= (5 sin (x) + 1) (5 sin (x) - 1)

= cos (7 x) (5 sin (x) + 1) (5 sin (x) - 1)

cos (7 x) (5 sin (x) + 1) (5 sin (x) - 1) = 0

各部分を別個に解く

cos (7 x) = 0 or 5 sin (x) + 1 = 0 or 5 sin (x) - 1 = 0

cos (7 x) = 0 : x = \frac{π}{14} + \frac{2 πn}{7}, x = \frac{3 π}{14} + \frac{2 πn}{7}

cos (7 x) = 0

以下の一般解

cos (7 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}

7 x = \frac{π}{2} + 2 πn, 7 x = \frac{3 π}{2} + 2 πn

7 x = \frac{π}{2} + 2 πn, 7 x = \frac{3 π}{2} + 2 πn

解く

7 x = \frac{π}{2} + 2 πn : x = \frac{π}{14} + \frac{2 πn}{7}

7 x = \frac{π}{2} + 2 πn

以下で両辺を割る

7

7 x = \frac{π}{2} + 2 πn

以下で両辺を割る

7

\frac{7 x}{7} = \frac{\frac{π}{2}}{7} + \frac{2 πn}{7}

簡素化

\frac{7 x}{7} = \frac{\frac{π}{2}}{7} + \frac{2 πn}{7}

簡素化

\frac{7 x}{7} : x

\frac{7 x}{7}

数を割る:

\frac{7}{7} = 1

= x

簡素化

\frac{\frac{π}{2}}{7} + \frac{2 πn}{7} : \frac{π}{14} + \frac{2 πn}{7}

\frac{\frac{π}{2}}{7} + \frac{2 πn}{7}

\frac{\frac{π}{2}}{7} = \frac{π}{14}

\frac{\frac{π}{2}}{7}

分数の規則を適用する:

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

= \frac{π}{2 \cdot 7}

数を乗じる:

2 \cdot 7 = 14

= \frac{π}{14}

= \frac{π}{14} + \frac{2 πn}{7}

x = \frac{π}{14} + \frac{2 πn}{7}

x = \frac{π}{14} + \frac{2 πn}{7}

x = \frac{π}{14} + \frac{2 πn}{7}

解く

7 x = \frac{3 π}{2} + 2 πn : x = \frac{3 π}{14} + \frac{2 πn}{7}

7 x = \frac{3 π}{2} + 2 πn

以下で両辺を割る

7

7 x = \frac{3 π}{2} + 2 πn

以下で両辺を割る

7

\frac{7 x}{7} = \frac{\frac{3 π}{2}}{7} + \frac{2 πn}{7}

簡素化

\frac{7 x}{7} = \frac{\frac{3 π}{2}}{7} + \frac{2 πn}{7}

簡素化

\frac{7 x}{7} : x

\frac{7 x}{7}

数を割る:

\frac{7}{7} = 1

= x

簡素化

\frac{\frac{3 π}{2}}{7} + \frac{2 πn}{7} : \frac{3 π}{14} + \frac{2 πn}{7}

\frac{\frac{3 π}{2}}{7} + \frac{2 πn}{7}

\frac{\frac{3 π}{2}}{7} = \frac{3 π}{14}

\frac{\frac{3 π}{2}}{7}

分数の規則を適用する:

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

= \frac{3 π}{2 \cdot 7}

数を乗じる:

2 \cdot 7 = 14

= \frac{3 π}{14}

= \frac{3 π}{14} + \frac{2 πn}{7}

x = \frac{3 π}{14} + \frac{2 πn}{7}

x = \frac{3 π}{14} + \frac{2 πn}{7}

x = \frac{3 π}{14} + \frac{2 πn}{7}

x = \frac{π}{14} + \frac{2 πn}{7}, x = \frac{3 π}{14} + \frac{2 πn}{7}

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

5 sin (x) + 1 = 0

1

を右側に移動します

5 sin (x) + 1 = 0

両辺から

1

を引く

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

簡素化

5 sin (x) = - 1

5 sin (x) = - 1

以下で両辺を割る

5

5 sin (x) = - 1

以下で両辺を割る

5

\frac{5 sin ( x )}{5} = \frac{- 1}{5}

簡素化

\frac{5 sin ( x )}{5} = \frac{- 1}{5}

簡素化

\frac{5 sin ( x )}{5} : sin (x)

\frac{5 sin ( x )}{5}

共通因数を約分する:

5

= sin (x)

簡素化

\frac{- 1}{5} : - \frac{5}{5}

\frac{- 1}{5}

分数の規則を適用する:

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

= - \frac{1}{5}

有理化する

- \frac{1}{5} : - \frac{5}{5}

- \frac{1}{5}

共役で乗じる

\frac{5}{5}

= - \frac{1 \cdot 5}{5 5}

1 \cdot 5 = 5

55 = 5

55

累乗根の規則を適用する:

a a = a

55 = 5

= 5

= - \frac{5}{5}

= - \frac{5}{5}

sin (x) = - \frac{5}{5}

sin (x) = - \frac{5}{5}

sin (x) = - \frac{5}{5}

三角関数の逆数プロパティを適用する

sin (x) = - \frac{5}{5}

以下の一般解

sin (x) = - \frac{5}{5}

sin (x) = - a \Rightarrow x = arcsin (- a) + 2 πn, x = π + arcsin (a) + 2 πn

x = arcsin (- \frac{5}{5}) + 2 πn, x = π + arcsin (\frac{5}{5}) + 2 πn

x = arcsin (- \frac{5}{5}) + 2 πn, x = π + arcsin (\frac{5}{5}) + 2 πn

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

5 sin (x) - 1 = 0

1

を右側に移動します

5 sin (x) - 1 = 0

両辺に

1

を足す

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

簡素化

5 sin (x) = 1

5 sin (x) = 1

以下で両辺を割る

5

5 sin (x) = 1

以下で両辺を割る

5

\frac{5 sin ( x )}{5} = \frac{1}{5}

簡素化

\frac{5 sin ( x )}{5} = \frac{1}{5}

簡素化

\frac{5 sin ( x )}{5} : sin (x)

\frac{5 sin ( x )}{5}

共通因数を約分する:

5

= sin (x)

簡素化

\frac{1}{5} : \frac{5}{5}

\frac{1}{5}

共役で乗じる

\frac{5}{5}

= \frac{1 \cdot 5}{5 5}

1 \cdot 5 = 5

55 = 5

55

累乗根の規則を適用する:

a a = a

55 = 5

= 5

= \frac{5}{5}

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

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

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

三角関数の逆数プロパティを適用する

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

以下の一般解

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

sin (x) = a \Rightarrow x = arcsin (a) + 2 πn, x = π - arcsin (a) + 2 πn

x = arcsin (\frac{5}{5}) + 2 πn, x = π - arcsin (\frac{5}{5}) + 2 πn

x = arcsin (\frac{5}{5}) + 2 πn, x = π - arcsin (\frac{5}{5}) + 2 πn

すべての解を組み合わせる

x = \frac{π}{14} + \frac{2 πn}{7}, x = \frac{3 π}{14} + \frac{2 πn}{7}, x = arcsin (- \frac{5}{5}) + 2 πn, x = π + arcsin (\frac{5}{5}) + 2 πn, x = arcsin (\frac{5}{5}) + 2 πn, x = π - arcsin (\frac{5}{5}) + 2 πn

10進法形式で解を証明する

x = \frac{π}{14} + \frac{2 πn}{7}, x = \frac{3 π}{14} + \frac{2 πn}{7}, x = - 0.46364 \dots + 2 πn, x = π + 0.46364 \dots + 2 πn, x = 0.46364 \dots + 2 πn, x = π - 0.46364 \dots + 2 πn

グラフ

人気の例

solvefor x,cos^2(x)*z^2-2cos^2(x)*z+1=0

so l v e f or x, cos^{2} (x) \cdot z^{2} - 2 cos^{2} (x) \cdot z + 1 = 0

sin(a)+sin(120+a)+sin(120-a)=0

sin (a) + sin (12 0^{\circ} + a) + sin (12 0^{\circ} - a) = 0

3sin(x)sin(x)=5cos(x)-2

3 sin (x) sin (x) = 5 cos (x) - 2

(cos(x)+3cos(x))/(2+2)=0

\frac{cos ( x ) + 3 cos ( x )}{2 + 2} = 0

3tan^3(x)-tan^2(x)-tan(x)-1=0

3 tan^{3} (x) - tan^{2} (x) - tan (x) - 1 = 0