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受欢迎的三角函数 >

(0.59.8l(1-cos(θ)))=0.018

解答

(0.5 \cdot 9.8 \cdot l (1 - cos (θ))) = 0.018

解答

θ = arccos (- \frac{9 - 2450 l}{2450 l}) + 2 πn, θ = - arccos (- \frac{9 - 2450 l}{2450 l}) + 2 πn

求解步骤

(0.5 \cdot 9.8 l (1 - cos (θ))) = 0.018

在两边乘以

1000

0.5 \cdot 9.8 l (1 - cos (θ)) = 0.018

To eliminate decimal points, multiply by 10 for every digit after the decimal pointThere are

3

digits to the right of the decimal point, therefore multiply by

1000

0.5 \cdot 9.8 l (1 - cos (θ)) \cdot 1000 = 0.018 \cdot 1000

整理后得

4900 l (1 - cos (θ)) = 18

4900 l (1 - cos (θ)) = 18

两边除以

4900 l; l \neq = 0

4900 l (1 - cos (θ)) = 18

两边除以

4900 l; l \neq = 0

\frac{4900 l ( 1 - cos ( θ ) )}{4900 l} = \frac{18}{4900 l}; l \neq = 0

化简

1 - cos (θ) = \frac{9}{2450 l}; l \neq = 0

1 - cos (θ) = \frac{9}{2450 l}; l \neq = 0

将

1

到右边

1 - cos (θ) = \frac{9}{2450 l}; l \neq = 0

两边减去

1

1 - cos (θ) - 1 = \frac{9}{2450 l} - 1; l \neq = 0

化简

- cos (θ) = \frac{9}{2450 l} - 1; l \neq = 0

- cos (θ) = \frac{9}{2450 l} - 1; l \neq = 0

两边除以

- 1; l \neq = 0

- cos (θ) = \frac{9}{2450 l} - 1; l \neq = 0

两边除以

- 1; l \neq = 0

\frac{- cos ( θ )}{- 1} = \frac{\frac{9}{2450 l}}{- 1} - \frac{1}{- 1}; l \neq = 0

化简

\frac{- cos ( θ )}{- 1} = \frac{\frac{9}{2450 l}}{- 1} - \frac{1}{- 1}

化简

\frac{- cos ( θ )}{- 1} : cos (θ)

\frac{- cos ( θ )}{- 1}

使用分式法则:

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

= \frac{cos ( θ )}{1}

使用法则

\frac{a}{1} = a

= cos (θ)

化简

\frac{\frac{9}{2450 l}}{- 1} - \frac{1}{- 1} : - \frac{9 - 2450 l}{2450 l}

\frac{\frac{9}{2450 l}}{- 1} - \frac{1}{- 1}

使用法则

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

= \frac{\frac{9}{2450 l} - 1}{- 1}

使用分式法则:

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

= - \frac{\frac{9}{2450 l} - 1}{1}

化简

\frac{9}{2450 l} - 1 : \frac{9 - 2450 l}{2450 l}

\frac{9}{2450 l} - 1

将项转换为分式:

1 = \frac{1 \cdot 2450 l}{2450 l}

= \frac{9}{2450 l} - \frac{1 \cdot 2450 l}{2450 l}

因为分母相等，所以合并分式:

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

= \frac{9 - 1 \cdot 2450 l}{2450 l}

数字相乘:

1 \cdot 2450 = 2450

= \frac{9 - 2450 l}{2450 l}

= - \frac{\frac{- 2450 l + 9}{2450 l}}{1}

使用分式法则:

\frac{a}{1} = a

= - \frac{- 2450 l + 9}{2450 l}

cos (θ) = - \frac{9 - 2450 l}{2450 l}; l \neq = 0

cos (θ) = - \frac{9 - 2450 l}{2450 l}; l \neq = 0

cos (θ) = - \frac{9 - 2450 l}{2450 l}; l \neq = 0

使用反三角函数性质

cos (θ) = - \frac{9 - 2450 l}{2450 l}

cos (θ) = - \frac{9 - 2450 l}{2450 l}

的通解

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

θ = arccos (- \frac{9 - 2450 l}{2450 l}) + 2 πn, θ = - arccos (- \frac{9 - 2450 l}{2450 l}) + 2 πn

θ = arccos (- \frac{9 - 2450 l}{2450 l}) + 2 πn, θ = - arccos (- \frac{9 - 2450 l}{2450 l}) + 2 πn

作图

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