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受欢迎的三角函数 >

solvefor x,c^2=a^2+b^2-2ab*cos(x)

解答

求解

x, c^{2} = a^{2} + b^{2} - 2 ab \cdot cos (x)

解答

x = arccos (- \frac{c ^{2} - a ^{2} - b ^{2}}{2 ab}) + 2 πn, x = - arccos (- \frac{c ^{2} - a ^{2} - b ^{2}}{2 ab}) + 2 πn

求解步骤

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

交换两边

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

将

a^{2}

到右边

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

两边减去

a^{2}

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

化简

b^{2} - 2 ab cos (x) = c^{2} - a^{2}

b^{2} - 2 ab cos (x) = c^{2} - a^{2}

将

b^{2}

到右边

b^{2} - 2 ab cos (x) = c^{2} - a^{2}

两边减去

b^{2}

b^{2} - 2 ab cos (x) - b^{2} = c^{2} - a^{2} - b^{2}

化简

- 2 ab cos (x) = c^{2} - a^{2} - b^{2}

- 2 ab cos (x) = c^{2} - a^{2} - b^{2}

两边除以

- 2 ab; - 2 ab \neq = 0

- 2 ab cos (x) = c^{2} - a^{2} - b^{2}

两边除以

- 2 ab; - 2 ab \neq = 0

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

化简

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

化简

\frac{- 2 ab cos ( x )}{- 2 ab} : cos (x)

\frac{- 2 ab cos ( x )}{- 2 ab}

使用分式法则:

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

= \frac{2 ab cos ( x )}{2 ab}

数字相除:

\frac{2}{2} = 1

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

约分:

a

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

约分:

b

= cos (x)

化简

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

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

使用法则

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

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

使用分式法则:

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

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

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

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

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

使用反三角函数性质

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

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

的通解

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

x = arccos (- \frac{c ^{2} - a ^{2} - b ^{2}}{2 ab}) + 2 πn, x = - arccos (- \frac{c ^{2} - a ^{2} - b ^{2}}{2 ab}) + 2 πn

x = arccos (- \frac{c ^{2} - a ^{2} - b ^{2}}{2 ab}) + 2 πn, x = - arccos (- \frac{c ^{2} - a ^{2} - b ^{2}}{2 ab}) + 2 πn

作图

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