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受欢迎的三角函数 >

7^2+25^2-2(7)(25)cos(x)=24^2

解答

7^{2} + 2 5^{2} - 2 (7) (25) cos (x) = 2 4^{2}

解答

x = 1.28700 \dots + 2 πn, x = 2 π - 1.28700 \dots + 2 πn

+1

度数

x = 73.73979 \dots^{\circ} + 36 0^{\circ} n, x = 286.26020 \dots^{\circ} + 36 0^{\circ} n

求解步骤

7^{2} + 2 5^{2} - 2 (7) (25) cos (x) = 2 4^{2}

数字相乘:

2 \cdot 7 \cdot 25 = 350

7^{2} + 2 5^{2} - 350 cos (x) = 2 4^{2}

7^{2} = 49

49 + 2 5^{2} - 350 cos (x) = 2 4^{2}

2 5^{2} = 625

49 + 625 - 350 cos (x) = 2 4^{2}

数字相加:

49 + 625 = 674

- 350 cos (x) + 674 = 2 4^{2}

2 4^{2} = 576

- 350 cos (x) + 674 = 576

将

674

到右边

- 350 cos (x) + 674 = 576

两边减去

674

- 350 cos (x) + 674 - 674 = 576 - 674

化简

- 350 cos (x) = - 98

- 350 cos (x) = - 98

两边除以

- 350

- 350 cos (x) = - 98

两边除以

- 350

\frac{- 350 cos ( x )}{- 350} = \frac{- 98}{- 350}

化简

\frac{- 350 cos ( x )}{- 350} = \frac{- 98}{- 350}

化简

\frac{- 350 cos ( x )}{- 350} : cos (x)

\frac{- 350 cos ( x )}{- 350}

使用分式法则:

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

= \frac{350 cos ( x )}{350}

数字相除:

\frac{350}{350} = 1

= cos (x)

化简

\frac{- 98}{- 350} : \frac{7}{25}

\frac{- 98}{- 350}

使用分式法则:

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

= \frac{98}{350}

约分:

14

= \frac{7}{25}

cos (x) = \frac{7}{25}

cos (x) = \frac{7}{25}

cos (x) = \frac{7}{25}

使用反三角函数性质

cos (x) = \frac{7}{25}

cos (x) = \frac{7}{25}

的通解

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

x = arccos (\frac{7}{25}) + 2 πn, x = 2 π - arccos (\frac{7}{25}) + 2 πn

x = arccos (\frac{7}{25}) + 2 πn, x = 2 π - arccos (\frac{7}{25}) + 2 πn

以小数形式表示解

x = 1.28700 \dots + 2 πn, x = 2 π - 1.28700 \dots + 2 πn

作图

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