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受欢迎的三角函数 >

10.5^2=6.7^2+7.8^2-26.77.8*cos(x)

解答

10. 5^{2} = 6. 7^{2} + 7. 8^{2} - 2 \cdot 6.7 \cdot 7.8 \cdot cos (x)

解答

x = 1.61405 \dots + 2 πn, x = - 1.61405 \dots + 2 πn

+1

度数

x = 92.47854 \dots^{\circ} + 36 0^{\circ} n, x = - 92.47854 \dots^{\circ} + 36 0^{\circ} n

求解步骤

10. 5^{2} = 6. 7^{2} + 7. 8^{2} - 2 \cdot 6.7 \cdot 7.8 cos (x)

交换两边

6. 7^{2} + 7. 8^{2} - 2 \cdot 6.7 \cdot 7.8 cos (x) = 10. 5^{2}

数字相乘:

2 \cdot 6.7 \cdot 7.8 = 104.52

6. 7^{2} + 7. 8^{2} - 104.52 cos (x) = 10. 5^{2}

6. 7^{2} = 44.89

44.89 + 7. 8^{2} - 104.52 cos (x) = 10. 5^{2}

7. 8^{2} = 60.84

44.89 + 60.84 - 104.52 cos (x) = 10. 5^{2}

数字相加:

44.89 + 60.84 = 105.73

- 104.52 cos (x) + 105.73 = 10. 5^{2}

10. 5^{2} = 110.25

- 104.52 cos (x) + 105.73 = 110.25

在两边乘以

100

- 104.52 cos (x) + 105.73 = 110.25

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

2

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

100

- 104.52 cos (x) \cdot 100 + 105.73 \cdot 100 = 110.25 \cdot 100

整理后得

- 10452 cos (x) + 10573 = 11025

- 10452 cos (x) + 10573 = 11025

将

10573

到右边

- 10452 cos (x) + 10573 = 11025

两边减去

10573

- 10452 cos (x) + 10573 - 10573 = 11025 - 10573

化简

- 10452 cos (x) = 452

- 10452 cos (x) = 452

两边除以

- 10452

- 10452 cos (x) = 452

两边除以

- 10452

\frac{- 10452 cos ( x )}{- 10452} = \frac{452}{- 10452}

化简

\frac{- 10452 cos ( x )}{- 10452} = \frac{452}{- 10452}

化简

\frac{- 10452 cos ( x )}{- 10452} : cos (x)

\frac{- 10452 cos ( x )}{- 10452}

使用分式法则:

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

= \frac{10452 cos ( x )}{10452}

数字相除:

\frac{10452}{10452} = 1

= cos (x)

化简

\frac{452}{- 10452} : - \frac{113}{2613}

\frac{452}{- 10452}

使用分式法则:

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

= - \frac{452}{10452}

约分:

4

= - \frac{113}{2613}

cos (x) = - \frac{113}{2613}

cos (x) = - \frac{113}{2613}

cos (x) = - \frac{113}{2613}

使用反三角函数性质

cos (x) = - \frac{113}{2613}

cos (x) = - \frac{113}{2613}

的通解

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

x = arccos (- \frac{113}{2613}) + 2 πn, x = - arccos (- \frac{113}{2613}) + 2 πn

x = arccos (- \frac{113}{2613}) + 2 πn, x = - arccos (- \frac{113}{2613}) + 2 πn

以小数形式表示解

x = 1.61405 \dots + 2 πn, x = - 1.61405 \dots + 2 πn

作图

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