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人気のある三角関数 >

solvefor b,a=arccos((a^2-b^2-c^2)/(-2bc))

解

解く

b, a = arccos (\frac{a ^{2} - b ^{2} - c ^{2}}{- 2 b c})

解

b = c cos (a) + c^{2} cos^{2} (a) - c^{2} + a^{2}, b = c cos (a) - c^{2} cos^{2} (a) - c^{2} + a^{2}

解答ステップ

a = arccos (\frac{a ^{2} - b ^{2} - c ^{2}}{- 2 b c})

辺を交換する

arccos (\frac{a ^{2} - b ^{2} - c ^{2}}{- 2 b c}) = a

三角関数の逆数プロパティを適用する

arccos (\frac{a ^{2} - b ^{2} - c ^{2}}{- 2 b c}) = a

arccos (x) = a \Rightarrow x = cos (a)

\frac{a ^{2} - b ^{2} - c ^{2}}{- 2 b c} = cos (a)

\frac{a ^{2} - b ^{2} - c ^{2}}{- 2 b c} = cos (a)

解く

\frac{a ^{2} - b ^{2} - c ^{2}}{- 2 b c} = cos (a) : b = c cos (a) + c^{2} cos^{2} (a) - c^{2} + a^{2}, b = c cos (a) - c^{2} cos^{2} (a) - c^{2} + a^{2}; c \neq = 0

\frac{a ^{2} - b ^{2} - c ^{2}}{- 2 b c} = cos (a)

簡素化

\frac{a ^{2} - b ^{2} - c ^{2}}{- 2 b c} : - \frac{a ^{2} - b ^{2} - c ^{2}}{2 b c}

\frac{a ^{2} - b ^{2} - c ^{2}}{- 2 b c}

分数の規則を適用する:

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

= - \frac{a ^{2} - b ^{2} - c ^{2}}{2 b c}

- \frac{a ^{2} - b ^{2} - c ^{2}}{2 b c} = cos (a)

以下で両辺を乗じる:

b

- \frac{a ^{2} - b ^{2} - c ^{2}}{2 b c} = cos (a)

以下で両辺を乗じる:

b

- \frac{a ^{2} - b ^{2} - c ^{2}}{2 b c} b = cos (a) b

簡素化

- \frac{a ^{2} - b ^{2} - c ^{2}}{2 c} = cos (a) b

- \frac{a ^{2} - b ^{2} - c ^{2}}{2 c} = cos (a) b

解く

- \frac{a ^{2} - b ^{2} - c ^{2}}{2 c} = cos (a) b : b = c cos (a) + c^{2} cos^{2} (a) - c^{2} + a^{2}, b = c cos (a) - c^{2} cos^{2} (a) - c^{2} + a^{2}

- \frac{a ^{2} - b ^{2} - c ^{2}}{2 c} = cos (a) b

以下で両辺を乗じる:

2 c

- \frac{a ^{2} - b ^{2} - c ^{2}}{2 c} = cos (a) b

以下で両辺を乗じる:

2 c

- \frac{a ^{2} - b ^{2} - c ^{2}}{2 c} \cdot 2 c = cos (a) b \cdot 2 c; c \neq = 0

簡素化

- (a^{2} - b^{2} - c^{2}) = 2 b c cos (a); c \neq = 0

- (a^{2} - b^{2} - c^{2}) = 2 b c cos (a); c \neq = 0

拡張

- (a^{2} - b^{2} - c^{2}) : - a^{2} + b^{2} + c^{2}

- (a^{2} - b^{2} - c^{2})

括弧を分配する

= - a^{2} - (- b^{2}) - (- c^{2})

マイナス・プラスの規則を適用する

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

= - a^{2} + b^{2} + c^{2}

- a^{2} + b^{2} + c^{2} = 2 b c cos (a); c \neq = 0

2 b c cos (a)

を左側に移動します

- a^{2} + b^{2} + c^{2} = 2 b c cos (a); c \neq = 0

両辺から

2 b c cos (a)

を引く

- a^{2} + b^{2} + c^{2} - 2 b c cos (a) = 2 b c cos (a) - 2 b c cos (a); c \neq = 0

簡素化

- a^{2} + b^{2} + c^{2} - 2 b c cos (a) = 0; c \neq = 0

- a^{2} + b^{2} + c^{2} - 2 b c cos (a) = 0; c \neq = 0

標準的な形式で書く

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

b^{2} - 2 c cos (a) b - a^{2} + c^{2} = 0; c \neq = 0

解くとthe二次式

b^{2} - 2 c cos (a) b - a^{2} + c^{2} = 0

二次Equationの公式:

次の場合:

a = 1, b = - 2 c cos (a), c = - a^{2} + c^{2}

b_{1, 2} = \frac{- ( - 2 c cos ( a ) ) \pm ( - 2 c cos ( a ) ) ^{2} - 4 \cdot 1 \cdot ( - a ^{2} + c ^{2} )}{2 \cdot 1}

b_{1, 2} = \frac{- ( - 2 c cos ( a ) ) \pm ( - 2 c cos ( a ) ) ^{2} - 4 \cdot 1 \cdot ( - a ^{2} + c ^{2} )}{2 \cdot 1}

簡素化

(- 2 c cos (a))^{2} - 4 \cdot 1 \cdot (- a^{2} + c^{2}) : 2 c^{2} cos^{2} (a) + a^{2} - c^{2}

(- 2 c cos (a))^{2} - 4 \cdot 1 \cdot (- a^{2} + c^{2})

(- 2 c cos (a))^{2} = 2^{2} c^{2} cos^{2} (a)

(- 2 c cos (a))^{2}

指数の規則を適用する:

n

が偶数であれば

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

(- 2 c cos (a))^{2} = (2 c cos (a))^{2}

= (2 c cos (a))^{2}

指数の規則を適用する:

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

= 2^{2} c^{2} cos^{2} (a)

4 \cdot 1 \cdot (- a^{2} + c^{2}) = 4 (- a^{2} + c^{2})

4 \cdot 1 \cdot (- a^{2} + c^{2})

数を乗じる:

4 \cdot 1 = 4

= 4 (c^{2} - a^{2})

= 2^{2} c^{2} cos^{2} (a) - 4 (c^{2} - a^{2})

因数

2^{2} c^{2} cos^{2} (a) - 4 (- a^{2} + c^{2}) : 4 (c^{2} cos^{2} (a) + a^{2} - c^{2})

2^{2} c^{2} cos^{2} (a) - 4 (- a^{2} + c^{2})

書き換え

= 4 c^{2} cos^{2} (a) - 4 (- a^{2} + c^{2})

共通項をくくり出す

4

= 4 (c^{2} cos^{2} (a) - (- a^{2} + c^{2}))

拡張

c^{2} cos^{2} (a) - (c^{2} - a^{2}) : c^{2} cos^{2} (a) + a^{2} - c^{2}

c^{2} cos^{2} (a) - (- a^{2} + c^{2})

- (- a^{2} + c^{2}) : a^{2} - c^{2}

- (- a^{2} + c^{2})

括弧を分配する

= - (- a^{2}) - c^{2}

マイナス・プラスの規則を適用する

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

= a^{2} - c^{2}

= c^{2} cos^{2} (a) + a^{2} - c^{2}

= 4 (c^{2} cos^{2} (a) - c^{2} + a^{2})

= 4 (c^{2} cos^{2} (a) + a^{2} - c^{2})

累乗根の規則を適用する:

n ab = n a n b,

, 以下を想定

a \geq 0, b \geq 0

= 4 c^{2} cos^{2} (a) - c^{2} + a^{2}

4 = 2

4

数を因数に分解する:

4 = 2^{2}

= 2^{2}

累乗根の規則を適用する:

n a^{n} = a

2^{2} = 2

= 2

= 2 c^{2} cos^{2} (a) - c^{2} + a^{2}

b_{1, 2} = \frac{- ( - 2 c cos ( a ) ) \pm 2 c ^{2} cos ^{2} ( a ) + a ^{2} - c ^{2}}{2 \cdot 1}

解を分離する

b_{1} = \frac{- ( - 2 c cos ( a ) ) + 2 c ^{2} cos ^{2} ( a ) + a ^{2} - c ^{2}}{2 \cdot 1}, b_{2} = \frac{- ( - 2 c cos ( a ) ) - 2 c ^{2} cos ^{2} ( a ) + a ^{2} - c ^{2}}{2 \cdot 1}

b = \frac{- ( - 2 c cos ( a ) ) + 2 c ^{2} cos ^{2} ( a ) + a ^{2} - c ^{2}}{2 \cdot 1} : c cos (a) + c^{2} cos^{2} (a) - c^{2} + a^{2}

\frac{- ( - 2 c cos ( a ) ) + 2 c ^{2} cos ^{2} ( a ) + a ^{2} - c ^{2}}{2 \cdot 1}

規則を適用

- (- a) = a

= \frac{2 c cos ( a ) + 2 c ^{2} cos ^{2} ( a ) + a ^{2} - c ^{2}}{2 \cdot 1}

数を乗じる:

2 \cdot 1 = 2

= \frac{2 c cos ( a ) + 2 c ^{2} cos ^{2} ( a ) - c ^{2} + a ^{2}}{2}

共通項をくくり出す

2

= \frac{2 ( c cos ( a ) + a ^{2} - c ^{2} + cos ^{2} ( a ) c ^{2} )}{2}

数を割る:

\frac{2}{2} = 1

= c cos (a) + c^{2} cos^{2} (a) - c^{2} + a^{2}

b = \frac{- ( - 2 c cos ( a ) ) - 2 c ^{2} cos ^{2} ( a ) + a ^{2} - c ^{2}}{2 \cdot 1} : c cos (a) - c^{2} cos^{2} (a) - c^{2} + a^{2}

\frac{- ( - 2 c cos ( a ) ) - 2 c ^{2} cos ^{2} ( a ) + a ^{2} - c ^{2}}{2 \cdot 1}

規則を適用

- (- a) = a

= \frac{2 c cos ( a ) - 2 c ^{2} cos ^{2} ( a ) + a ^{2} - c ^{2}}{2 \cdot 1}

数を乗じる:

2 \cdot 1 = 2

= \frac{2 c cos ( a ) - 2 c ^{2} cos ^{2} ( a ) - c ^{2} + a ^{2}}{2}

共通項をくくり出す

2

= \frac{2 ( c cos ( a ) - a ^{2} - c ^{2} + cos ^{2} ( a ) c ^{2} )}{2}

数を割る:

\frac{2}{2} = 1

= c cos (a) - c^{2} cos^{2} (a) - c^{2} + a^{2}

二次equationの解:

b = c cos (a) + c^{2} cos^{2} (a) - c^{2} + a^{2}, b = c cos (a) - c^{2} cos^{2} (a) - c^{2} + a^{2}

b = c cos (a) + c^{2} cos^{2} (a) - c^{2} + a^{2}, b = c cos (a) - c^{2} cos^{2} (a) - c^{2} + a^{2}; c \neq = 0

b = c cos (a) + c^{2} cos^{2} (a) - c^{2} + a^{2}, b = c cos (a) - c^{2} cos^{2} (a) - c^{2} + a^{2}

グラフ

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