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受欢迎的三角函数 >

58.2^2=25.8^2+33.4^2-2(25.8(33.4))cos(a)

解答

58. 2^{2} = 25. 8^{2} + 33. 4^{2} - 2 (25.8 (33.4)) cos (a)

解答

a = 2.77035 \dots + 2 πn, a = - 2.77035 \dots + 2 πn

+1

度数

a = 158.72986 \dots^{\circ} + 36 0^{\circ} n, a = - 158.72986 \dots^{\circ} + 36 0^{\circ} n

求解步骤

58. 2^{2} = 25. 8^{2} + 33. 4^{2} - 2 (25.8 (33.4)) cos (a)

交换两边

25. 8^{2} + 33. 4^{2} - 2 \cdot 25.8 \cdot 33.4 cos (a) = 58. 2^{2}

数字相乘:

2 \cdot 25.8 \cdot 33.4 = 1723.44

25. 8^{2} + 33. 4^{2} - 1723.44 cos (a) = 58. 2^{2}

25. 8^{2} = 665.64

665.64 + 33. 4^{2} - 1723.44 cos (a) = 58. 2^{2}

33. 4^{2} = 1115.56

665.64 + 1115.56 - 1723.44 cos (a) = 58. 2^{2}

数字相加:

665.64 + 1115.56 = 1781.2

- 1723.44 cos (a) + 1781.2 = 58. 2^{2}

58. 2^{2} = 3387.24

- 1723.44 cos (a) + 1781.2 = 3387.24

在两边乘以

100

- 1723.44 cos (a) + 1781.2 = 3387.24

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

- 1723.44 cos (a) \cdot 100 + 1781.2 \cdot 100 = 3387.24 \cdot 100

整理后得

- 172344 cos (a) + 178120 = 338724

- 172344 cos (a) + 178120 = 338724

将

178120

到右边

- 172344 cos (a) + 178120 = 338724

两边减去

178120

- 172344 cos (a) + 178120 - 178120 = 338724 - 178120

化简

- 172344 cos (a) = 160604

- 172344 cos (a) = 160604

两边除以

- 172344

- 172344 cos (a) = 160604

两边除以

- 172344

\frac{- 172344 cos ( a )}{- 172344} = \frac{160604}{- 172344}

化简

\frac{- 172344 cos ( a )}{- 172344} = \frac{160604}{- 172344}

化简

\frac{- 172344 cos ( a )}{- 172344} : cos (a)

\frac{- 172344 cos ( a )}{- 172344}

使用分式法则:

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

= \frac{172344 cos ( a )}{172344}

数字相除:

\frac{172344}{172344} = 1

= cos (a)

化简

\frac{160604}{- 172344} : - \frac{40151}{43086}

\frac{160604}{- 172344}

使用分式法则:

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

= - \frac{160604}{172344}

约分:

4

= - \frac{40151}{43086}

cos (a) = - \frac{40151}{43086}

cos (a) = - \frac{40151}{43086}

cos (a) = - \frac{40151}{43086}

使用反三角函数性质

cos (a) = - \frac{40151}{43086}

cos (a) = - \frac{40151}{43086}

的通解

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

a = arccos (- \frac{40151}{43086}) + 2 πn, a = - arccos (- \frac{40151}{43086}) + 2 πn

a = arccos (- \frac{40151}{43086}) + 2 πn, a = - arccos (- \frac{40151}{43086}) + 2 πn

以小数形式表示解

a = 2.77035 \dots + 2 πn, a = - 2.77035 \dots + 2 πn

作图

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