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 >

solvefor g,θ(t)=-1cos(sqrt(g/l)t)

解

解く

g, θ (t) = - 1 cos (\frac{g}{l} t)

解

g = \frac{l arccos ^{2} ( - θt )}{t ^{2}} + \frac{4 π l n arccos ( - θt )}{t ^{2}} + \frac{4 π ^{2} l n ^{2}}{t ^{2}}, g = \frac{l arccos ^{2} ( - θt )}{t ^{2}} - \frac{4 π l n arccos ( - θt )}{t ^{2}} + \frac{4 π ^{2} l n ^{2}}{t ^{2}}

解答ステップ

θ (t) = - 1 \cdot cos (\frac{g}{l} t)

辺を交換する

- 1 \cdot cos (\frac{g}{l} t) = θt

以下で両辺を割る

- 1

- 1 \cdot cos (\frac{g}{l} t) = θt

以下で両辺を割る

- 1

\frac{- 1 \cdot cos ( \frac{g}{l} t )}{- 1} = \frac{θt}{- 1}

簡素化

cos (\frac{g}{l} t) = - θt

cos (\frac{g}{l} t) = - θt

三角関数の逆数プロパティを適用する

cos (\frac{g}{l} t) = - θt

以下の一般解

cos (\frac{g}{l} t) = - θt

cos (x) = a \Rightarrow x = arccos (a) + 2 πn, x = - arccos (a) + 2 πn

\frac{g}{l} t = arccos (- θt) + 2 πn, \frac{g}{l} t = - arccos (- θt) + 2 πn

\frac{g}{l} t = arccos (- θt) + 2 πn, \frac{g}{l} t = - arccos (- θt) + 2 πn

解く

\frac{g}{l} t = arccos (- θt) + 2 πn : g = \frac{l arccos ^{2} ( - θt )}{t ^{2}} + \frac{4 π l n arccos ( - θt )}{t ^{2}} + \frac{4 π ^{2} l n ^{2}}{t ^{2}}

\frac{g}{l} t = arccos (- θt) + 2 πn

以下で両辺を割る

t

\frac{g}{l} t = arccos (- θt) + 2 πn

以下で両辺を割る

t

\frac{\frac{g}{l} t}{t} = \frac{arccos ( - θt )}{t} + \frac{2 πn}{t}

簡素化

\frac{g}{l} = \frac{arccos ( - θt )}{t} + \frac{2 πn}{t}

\frac{g}{l} = \frac{arccos ( - θt )}{t} + \frac{2 πn}{t}

両辺を2乗する:

\frac{g}{l} = \frac{arccos ^{2} ( - θt )}{t ^{2}} + \frac{4 πn arccos ( - θt )}{t ^{2}} + \frac{4 π ^{2} n ^{2}}{t ^{2}}

\frac{g}{l} = \frac{arccos ( - θt )}{t} + \frac{2 πn}{t}

(\frac{g}{l})^{2} = (\frac{arccos ( - θt )}{t} + \frac{2 πn}{t})^{2}

拡張

(\frac{g}{l})^{2} : \frac{g}{l}

(\frac{g}{l})^{2}

累乗根の規則を適用する:

a = a^{\frac{1}{2}}

= ((\frac{g}{l})^{\frac{1}{2}})^{2}

指数の規則を適用する:

(a^{b})^{c} = a^{b c}

= (\frac{g}{l})^{\frac{1}{2} \cdot 2}

\frac{1}{2} \cdot 2 = 1

\frac{1}{2} \cdot 2

分数を乗じる:

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

= \frac{1 \cdot 2}{2}

共通因数を約分する:

2

= 1

= \frac{g}{l}

拡張

(\frac{arccos ( - θt )}{t} + \frac{2 πn}{t})^{2} : \frac{arccos ^{2} ( - θt )}{t ^{2}} + \frac{4 πn arccos ( - θt )}{t ^{2}} + \frac{4 π ^{2} n ^{2}}{t ^{2}}

(\frac{arccos ( - θt )}{t} + \frac{2 πn}{t})^{2}

分数を組み合わせる

\frac{arccos ( - θt )}{t} + \frac{2 πn}{t} : \frac{arccos ( - θt ) + 2 πn}{t}

規則を適用

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

= \frac{arccos ( - θt ) + 2 πn}{t}

= (\frac{arccos ( - θt ) + 2 πn}{t})^{2}

指数の規則を適用する:

(\frac{a}{b})^{c} = \frac{a ^{c}}{b ^{c}}

= \frac{( arccos ( - θt ) + 2 πn ) ^{2}}{t ^{2}}

(arccos (- θt) + 2 πn)^{2} = arccos^{2} (- θt) + 4 πn arccos (- θt) + 4 π^{2} n^{2}

(arccos (- θt) + 2 πn)^{2}

完全平方式を適用する:

(a + b)^{2} = a^{2} + 2 ab + b^{2}

a = arccos (- θt), b = 2 πn

= arccos^{2} (- θt) + 2 arccos (- θt) \cdot 2 πn + (2 πn)^{2}

簡素化

arccos^{2} (- θt) + 2 arccos (- θt) \cdot 2 πn + (2 πn)^{2} : arccos^{2} (- θt) + 4 πn arccos (- θt) + 4 π^{2} n^{2}

arccos^{2} (- θt) + 2 arccos (- θt) \cdot 2 πn + (2 πn)^{2}

2 arccos (- θt) \cdot 2 πn = 4 πn arccos (- θt)

2 arccos (- θt) \cdot 2 πn

数を乗じる:

2 \cdot 2 = 4

= 4 πn arccos (- θt)

(2 πn)^{2} = 4 π^{2} n^{2}

(2 πn)^{2}

指数の規則を適用する:

(a \cdot b)^{n} = a^{n} b^{n}

= 2^{2} π^{2} n^{2}

2^{2} = 4

= 4 π^{2} n^{2}

= arccos^{2} (- θt) + 4 πn arccos (- θt) + 4 π^{2} n^{2}

= arccos^{2} (- θt) + 4 πn arccos (- θt) + 4 π^{2} n^{2}

= \frac{arccos ^{2} ( - θt ) + 4 πn arccos ( - θt ) + 4 π ^{2} n ^{2}}{t ^{2}}

分数の規則を適用する:

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

\frac{arccos ^{2} ( - θt ) + 4 πn arccos ( - θt ) + 4 π ^{2} n ^{2}}{t ^{2}} = \frac{arccos ^{2} ( - θt )}{t ^{2}} + \frac{4 πn arccos ( - θt )}{t ^{2}} + \frac{4 π ^{2} n ^{2}}{t ^{2}}

= \frac{arccos ^{2} ( - θt )}{t ^{2}} + \frac{4 πn arccos ( - θt )}{t ^{2}} + \frac{4 π ^{2} n ^{2}}{t ^{2}}

\frac{g}{l} = \frac{arccos ^{2} ( - θt )}{t ^{2}} + \frac{4 πn arccos ( - θt )}{t ^{2}} + \frac{4 π ^{2} n ^{2}}{t ^{2}}

\frac{g}{l} = \frac{arccos ^{2} ( - θt )}{t ^{2}} + \frac{4 πn arccos ( - θt )}{t ^{2}} + \frac{4 π ^{2} n ^{2}}{t ^{2}}

解く

\frac{g}{l} = \frac{arccos ^{2} ( - θt )}{t ^{2}} + \frac{4 πn arccos ( - θt )}{t ^{2}} + \frac{4 π ^{2} n ^{2}}{t ^{2}} : g = \frac{l arccos ^{2} ( - θt )}{t ^{2}} + \frac{4 π l n arccos ( - θt )}{t ^{2}} + \frac{4 π ^{2} l n ^{2}}{t ^{2}}

\frac{g}{l} = \frac{arccos ^{2} ( - θt )}{t ^{2}} + \frac{4 πn arccos ( - θt )}{t ^{2}} + \frac{4 π ^{2} n ^{2}}{t ^{2}}

以下で両辺を乗じる:

l

\frac{g}{l} = \frac{arccos ^{2} ( - θt )}{t ^{2}} + \frac{4 πn arccos ( - θt )}{t ^{2}} + \frac{4 π ^{2} n ^{2}}{t ^{2}}

以下で両辺を乗じる:

l

\frac{g l}{l} = \frac{arccos ^{2} ( - θt )}{t ^{2}} l + \frac{4 πn arccos ( - θt )}{t ^{2}} l + \frac{4 π ^{2} n ^{2}}{t ^{2}} l

簡素化

\frac{g l}{l} = \frac{arccos ^{2} ( - θt )}{t ^{2}} l + \frac{4 πn arccos ( - θt )}{t ^{2}} l + \frac{4 π ^{2} n ^{2}}{t ^{2}} l

簡素化

\frac{g l}{l} : g

\frac{g l}{l}

共通因数を約分する:

l

= g

簡素化

\frac{arccos ^{2} ( - θt )}{t ^{2}} l + \frac{4 πn arccos ( - θt )}{t ^{2}} l + \frac{4 π ^{2} n ^{2}}{t ^{2}} l : \frac{l arccos ^{2} ( - θt )}{t ^{2}} + \frac{4 π l n arccos ( - θt )}{t ^{2}} + \frac{4 π ^{2} l n ^{2}}{t ^{2}}

\frac{arccos ^{2} ( - θt )}{t ^{2}} l + \frac{4 πn arccos ( - θt )}{t ^{2}} l + \frac{4 π ^{2} n ^{2}}{t ^{2}} l

乗じる

\frac{arccos ^{2} ( - θt )}{t ^{2}} l : \frac{l arccos ^{2} ( - θt )}{t ^{2}}

\frac{arccos ^{2} ( - θt )}{t ^{2}} l

分数を乗じる:

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

= \frac{arccos ^{2} ( - θt ) l}{t ^{2}}

= \frac{l arccos ^{2} ( - θt )}{t ^{2}} + l \frac{4 πn arccos ( - θt )}{t ^{2}} + l \frac{4 π ^{2} n ^{2}}{t ^{2}}

乗じる

\frac{4 πn arccos ( - θt )}{t ^{2}} l : \frac{4 π l n arccos ( - θt )}{t ^{2}}

\frac{4 πn arccos ( - θt )}{t ^{2}} l

分数を乗じる:

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

= \frac{4 πn arccos ( - θt ) l}{t ^{2}}

= \frac{l arccos ^{2} ( - θt )}{t ^{2}} + \frac{4 π l n arccos ( - θt )}{t ^{2}} + l \frac{4 π ^{2} n ^{2}}{t ^{2}}

乗じる

\frac{4 π ^{2} n ^{2}}{t ^{2}} l : \frac{4 π ^{2} l n ^{2}}{t ^{2}}

\frac{4 π ^{2} n ^{2}}{t ^{2}} l

分数を乗じる:

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

= \frac{4 π ^{2} n ^{2} l}{t ^{2}}

= \frac{l arccos ^{2} ( - θt )}{t ^{2}} + \frac{4 π l n arccos ( - θt )}{t ^{2}} + \frac{4 π ^{2} l n ^{2}}{t ^{2}}

g = \frac{l arccos ^{2} ( - θt )}{t ^{2}} + \frac{4 π l n arccos ( - θt )}{t ^{2}} + \frac{4 π ^{2} l n ^{2}}{t ^{2}}

g = \frac{l arccos ^{2} ( - θt )}{t ^{2}} + \frac{4 π l n arccos ( - θt )}{t ^{2}} + \frac{4 π ^{2} l n ^{2}}{t ^{2}}

g = \frac{l arccos ^{2} ( - θt )}{t ^{2}} + \frac{4 π l n arccos ( - θt )}{t ^{2}} + \frac{4 π ^{2} l n ^{2}}{t ^{2}}

g = \frac{l arccos ^{2} ( - θt )}{t ^{2}} + \frac{4 π l n arccos ( - θt )}{t ^{2}} + \frac{4 π ^{2} l n ^{2}}{t ^{2}}

解く

\frac{g}{l} t = - arccos (- θt) + 2 πn : g = \frac{l arccos ^{2} ( - θt )}{t ^{2}} - \frac{4 π l n arccos ( - θt )}{t ^{2}} + \frac{4 π ^{2} l n ^{2}}{t ^{2}}

\frac{g}{l} t = - arccos (- θt) + 2 πn

以下で両辺を割る

t

\frac{g}{l} t = - arccos (- θt) + 2 πn

以下で両辺を割る

t

\frac{\frac{g}{l} t}{t} = - \frac{arccos ( - θt )}{t} + \frac{2 πn}{t}

簡素化

\frac{g}{l} = - \frac{arccos ( - θt )}{t} + \frac{2 πn}{t}

\frac{g}{l} = - \frac{arccos ( - θt )}{t} + \frac{2 πn}{t}

両辺を2乗する:

\frac{g}{l} = \frac{arccos ^{2} ( - θt )}{t ^{2}} - \frac{4 πn arccos ( - θt )}{t ^{2}} + \frac{4 π ^{2} n ^{2}}{t ^{2}}

\frac{g}{l} = - \frac{arccos ( - θt )}{t} + \frac{2 πn}{t}

(\frac{g}{l})^{2} = (- \frac{arccos ( - θt )}{t} + \frac{2 πn}{t})^{2}

拡張

(\frac{g}{l})^{2} : \frac{g}{l}

(\frac{g}{l})^{2}

累乗根の規則を適用する:

a = a^{\frac{1}{2}}

= ((\frac{g}{l})^{\frac{1}{2}})^{2}

指数の規則を適用する:

(a^{b})^{c} = a^{b c}

= (\frac{g}{l})^{\frac{1}{2} \cdot 2}

\frac{1}{2} \cdot 2 = 1

\frac{1}{2} \cdot 2

分数を乗じる:

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

= \frac{1 \cdot 2}{2}

共通因数を約分する:

2

= 1

= \frac{g}{l}

拡張

(- \frac{arccos ( - θt )}{t} + \frac{2 πn}{t})^{2} : \frac{arccos ^{2} ( - θt )}{t ^{2}} - \frac{4 πn arccos ( - θt )}{t ^{2}} + \frac{4 π ^{2} n ^{2}}{t ^{2}}

(- \frac{arccos ( - θt )}{t} + \frac{2 πn}{t})^{2}

分数を組み合わせる

- \frac{arccos ( - θt )}{t} + \frac{2 πn}{t} : \frac{- arccos ( - θt ) + 2 πn}{t}

規則を適用

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

= \frac{- arccos ( - θt ) + 2 πn}{t}

= (\frac{- arccos ( - θt ) + 2 πn}{t})^{2}

指数の規則を適用する:

(\frac{a}{b})^{c} = \frac{a ^{c}}{b ^{c}}

= \frac{( - arccos ( - θt ) + 2 πn ) ^{2}}{t ^{2}}

(- arccos (- θt) + 2 πn)^{2} = arccos^{2} (- θt) - 4 πn arccos (- θt) + 4 π^{2} n^{2}

(- arccos (- θt) + 2 πn)^{2}

完全平方式を適用する:

(a + b)^{2} = a^{2} + 2 ab + b^{2}

a = - arccos (- θt), b = 2 πn

= (- arccos (- θt))^{2} + 2 (- arccos (- θt)) \cdot 2 πn + (2 πn)^{2}

簡素化

(- arccos (- θt))^{2} + 2 (- arccos (- θt)) \cdot 2 πn + (2 πn)^{2} : arccos^{2} (- θt) - 4 πn arccos (- θt) + 4 π^{2} n^{2}

(- arccos (- θt))^{2} + 2 (- arccos (- θt)) \cdot 2 πn + (2 πn)^{2}

括弧を削除する:

(- a) = - a

= (- arccos (- θt))^{2} - 2 arccos (- θt) \cdot 2 πn + (2 πn)^{2}

(- arccos (- θt))^{2} = arccos^{2} (- θt)

(- arccos (- θt))^{2}

指数の規則を適用する:

n

が偶数であれば

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

(- arccos (- θt))^{2} = arccos^{2} (- θt)

= arccos^{2} (- θt)

2 arccos (- θt) \cdot 2 πn = 4 πn arccos (- θt)

2 arccos (- θt) \cdot 2 πn

数を乗じる:

2 \cdot 2 = 4

= 4 πn arccos (- θt)

(2 πn)^{2} = 4 π^{2} n^{2}

(2 πn)^{2}

指数の規則を適用する:

(a \cdot b)^{n} = a^{n} b^{n}

= 2^{2} π^{2} n^{2}

2^{2} = 4

= 4 π^{2} n^{2}

= arccos^{2} (- θt) - 4 πn arccos (- θt) + 4 π^{2} n^{2}

= arccos^{2} (- θt) - 4 πn arccos (- θt) + 4 π^{2} n^{2}

= \frac{arccos ^{2} ( - θt ) - 4 πn arccos ( - θt ) + 4 π ^{2} n ^{2}}{t ^{2}}

分数の規則を適用する:

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

\frac{arccos ^{2} ( - θt ) - 4 πn arccos ( - θt ) + 4 π ^{2} n ^{2}}{t ^{2}} = \frac{arccos ^{2} ( - θt )}{t ^{2}} - \frac{4 πn arccos ( - θt )}{t ^{2}} + \frac{4 π ^{2} n ^{2}}{t ^{2}}

= \frac{arccos ^{2} ( - θt )}{t ^{2}} - \frac{4 πn arccos ( - θt )}{t ^{2}} + \frac{4 π ^{2} n ^{2}}{t ^{2}}

\frac{g}{l} = \frac{arccos ^{2} ( - θt )}{t ^{2}} - \frac{4 πn arccos ( - θt )}{t ^{2}} + \frac{4 π ^{2} n ^{2}}{t ^{2}}

\frac{g}{l} = \frac{arccos ^{2} ( - θt )}{t ^{2}} - \frac{4 πn arccos ( - θt )}{t ^{2}} + \frac{4 π ^{2} n ^{2}}{t ^{2}}

解く

\frac{g}{l} = \frac{arccos ^{2} ( - θt )}{t ^{2}} - \frac{4 πn arccos ( - θt )}{t ^{2}} + \frac{4 π ^{2} n ^{2}}{t ^{2}} : g = \frac{l arccos ^{2} ( - θt )}{t ^{2}} - \frac{4 π l n arccos ( - θt )}{t ^{2}} + \frac{4 π ^{2} l n ^{2}}{t ^{2}}

\frac{g}{l} = \frac{arccos ^{2} ( - θt )}{t ^{2}} - \frac{4 πn arccos ( - θt )}{t ^{2}} + \frac{4 π ^{2} n ^{2}}{t ^{2}}

以下で両辺を乗じる:

l

\frac{g}{l} = \frac{arccos ^{2} ( - θt )}{t ^{2}} - \frac{4 πn arccos ( - θt )}{t ^{2}} + \frac{4 π ^{2} n ^{2}}{t ^{2}}

以下で両辺を乗じる:

l

\frac{g l}{l} = \frac{arccos ^{2} ( - θt )}{t ^{2}} l - \frac{4 πn arccos ( - θt )}{t ^{2}} l + \frac{4 π ^{2} n ^{2}}{t ^{2}} l

簡素化

\frac{g l}{l} = \frac{arccos ^{2} ( - θt )}{t ^{2}} l - \frac{4 πn arccos ( - θt )}{t ^{2}} l + \frac{4 π ^{2} n ^{2}}{t ^{2}} l

簡素化

\frac{g l}{l} : g

\frac{g l}{l}

共通因数を約分する:

l

= g

簡素化

\frac{arccos ^{2} ( - θt )}{t ^{2}} l - \frac{4 πn arccos ( - θt )}{t ^{2}} l + \frac{4 π ^{2} n ^{2}}{t ^{2}} l : \frac{l arccos ^{2} ( - θt )}{t ^{2}} - \frac{4 π l n arccos ( - θt )}{t ^{2}} + \frac{4 π ^{2} l n ^{2}}{t ^{2}}

\frac{arccos ^{2} ( - θt )}{t ^{2}} l - \frac{4 πn arccos ( - θt )}{t ^{2}} l + \frac{4 π ^{2} n ^{2}}{t ^{2}} l

乗じる

\frac{arccos ^{2} ( - θt )}{t ^{2}} l : \frac{l arccos ^{2} ( - θt )}{t ^{2}}

\frac{arccos ^{2} ( - θt )}{t ^{2}} l

分数を乗じる:

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

= \frac{arccos ^{2} ( - θt ) l}{t ^{2}}

= \frac{l arccos ^{2} ( - θt )}{t ^{2}} - l \frac{4 πn arccos ( - θt )}{t ^{2}} + l \frac{4 π ^{2} n ^{2}}{t ^{2}}

乗じる

\frac{4 πn arccos ( - θt )}{t ^{2}} l : \frac{4 π l n arccos ( - θt )}{t ^{2}}

\frac{4 πn arccos ( - θt )}{t ^{2}} l

分数を乗じる:

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

= \frac{4 πn arccos ( - θt ) l}{t ^{2}}

= \frac{l arccos ^{2} ( - θt )}{t ^{2}} - \frac{4 π l n arccos ( - θt )}{t ^{2}} + l \frac{4 π ^{2} n ^{2}}{t ^{2}}

乗じる

\frac{4 π ^{2} n ^{2}}{t ^{2}} l : \frac{4 π ^{2} l n ^{2}}{t ^{2}}

\frac{4 π ^{2} n ^{2}}{t ^{2}} l

分数を乗じる:

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

= \frac{4 π ^{2} n ^{2} l}{t ^{2}}

= \frac{l arccos ^{2} ( - θt )}{t ^{2}} - \frac{4 π l n arccos ( - θt )}{t ^{2}} + \frac{4 π ^{2} l n ^{2}}{t ^{2}}

g = \frac{l arccos ^{2} ( - θt )}{t ^{2}} - \frac{4 π l n arccos ( - θt )}{t ^{2}} + \frac{4 π ^{2} l n ^{2}}{t ^{2}}

g = \frac{l arccos ^{2} ( - θt )}{t ^{2}} - \frac{4 π l n arccos ( - θt )}{t ^{2}} + \frac{4 π ^{2} l n ^{2}}{t ^{2}}

g = \frac{l arccos ^{2} ( - θt )}{t ^{2}} - \frac{4 π l n arccos ( - θt )}{t ^{2}} + \frac{4 π ^{2} l n ^{2}}{t ^{2}}

g = \frac{l arccos ^{2} ( - θt )}{t ^{2}} - \frac{4 π l n arccos ( - θt )}{t ^{2}} + \frac{4 π ^{2} l n ^{2}}{t ^{2}}

g = \frac{l arccos ^{2} ( - θt )}{t ^{2}} + \frac{4 π l n arccos ( - θt )}{t ^{2}} + \frac{4 π ^{2} l n ^{2}}{t ^{2}}, g = \frac{l arccos ^{2} ( - θt )}{t ^{2}} - \frac{4 π l n arccos ( - θt )}{t ^{2}} + \frac{4 π ^{2} l n ^{2}}{t ^{2}}

グラフ

人気の例

sec (x) = - 3

2tan(x)csc(x)+2csc(x)+tan(x)+1=0

2 tan (x) csc (x) + 2 csc (x) + tan (x) + 1 = 0

csc(x)+cot(x)=sqrt(3),0<= x<= 2pi

csc (x) + cot (x) = 3, 0 \leq x \leq 2 π

(tan^2(x)-4)(2cos(x)+1)=0

(tan^{2} (x) - 4) (2 cos (x) + 1) = 0

cos (a) = \frac{1}{4}