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受欢迎的三角函数 >

12^{(2)}=13^{(2)}+5^{(2)}-2(13)(5)cos(B)

解答

1 2^{(2)} = 1 3^{(2)} + 5^{(2)} - 2 (13) (5) cos (B)

解答

B = 1.17600 \dots + 2 πn, B = 2 π - 1.17600 \dots + 2 πn

+1

度数

B = 67.38013 \dots^{\circ} + 36 0^{\circ} n, B = 292.61986 \dots^{\circ} + 36 0^{\circ} n

求解步骤

1 2^{(2)} = 1 3^{(2)} + 5^{(2)} - 2 (13) (5) cos (B)

交换两边

1 3^{2} + 5^{2} - 2 \cdot 13 \cdot 5 cos (B) = 1 2^{2}

数字相乘:

2 \cdot 13 \cdot 5 = 130

1 3^{2} + 5^{2} - 130 cos (B) = 1 2^{2}

1 3^{2} = 169

169 + 5^{2} - 130 cos (B) = 1 2^{2}

5^{2} = 25

169 + 25 - 130 cos (B) = 1 2^{2}

数字相加:

169 + 25 = 194

- 130 cos (B) + 194 = 1 2^{2}

1 2^{2} = 144

- 130 cos (B) + 194 = 144

将

194

到右边

- 130 cos (B) + 194 = 144

两边减去

194

- 130 cos (B) + 194 - 194 = 144 - 194

化简

- 130 cos (B) = - 50

- 130 cos (B) = - 50

两边除以

- 130

- 130 cos (B) = - 50

两边除以

- 130

\frac{- 130 cos ( B )}{- 130} = \frac{- 50}{- 130}

化简

\frac{- 130 cos ( B )}{- 130} = \frac{- 50}{- 130}

化简

\frac{- 130 cos ( B )}{- 130} : cos (B)

\frac{- 130 cos ( B )}{- 130}

使用分式法则:

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

= \frac{130 cos ( B )}{130}

数字相除:

\frac{130}{130} = 1

= cos (B)

化简

\frac{- 50}{- 130} : \frac{5}{13}

\frac{- 50}{- 130}

使用分式法则:

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

= \frac{50}{130}

约分:

10

= \frac{5}{13}

cos (B) = \frac{5}{13}

cos (B) = \frac{5}{13}

cos (B) = \frac{5}{13}

使用反三角函数性质

cos (B) = \frac{5}{13}

cos (B) = \frac{5}{13}

的通解

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

B = arccos (\frac{5}{13}) + 2 πn, B = 2 π - arccos (\frac{5}{13}) + 2 πn

B = arccos (\frac{5}{13}) + 2 πn, B = 2 π - arccos (\frac{5}{13}) + 2 πn

以小数形式表示解

B = 1.17600 \dots + 2 πn, B = 2 π - 1.17600 \dots + 2 πn

作图

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