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受欢迎的三角函数 >

40^2=28^2+15^2-2(28)(15)*cos(x)

解答

4 0^{2} = 2 8^{2} + 1 5^{2} - 2 (28) (15) \cdot cos (x)

解答

x = 2.35120 \dots + 2 πn, x = - 2.35120 \dots + 2 πn

+1

度数

x = 134.71424 \dots^{\circ} + 36 0^{\circ} n, x = - 134.71424 \dots^{\circ} + 36 0^{\circ} n

求解步骤

4 0^{2} = 2 8^{2} + 1 5^{2} - 2 (28) (15) cos (x)

交换两边

2 8^{2} + 1 5^{2} - 2 \cdot 28 \cdot 15 cos (x) = 4 0^{2}

数字相乘:

2 \cdot 28 \cdot 15 = 840

2 8^{2} + 1 5^{2} - 840 cos (x) = 4 0^{2}

2 8^{2} = 784

784 + 1 5^{2} - 840 cos (x) = 4 0^{2}

1 5^{2} = 225

784 + 225 - 840 cos (x) = 4 0^{2}

数字相加:

784 + 225 = 1009

- 840 cos (x) + 1009 = 4 0^{2}

4 0^{2} = 1600

- 840 cos (x) + 1009 = 1600

将

1009

到右边

- 840 cos (x) + 1009 = 1600

两边减去

1009

- 840 cos (x) + 1009 - 1009 = 1600 - 1009

化简

- 840 cos (x) = 591

- 840 cos (x) = 591

两边除以

- 840

- 840 cos (x) = 591

两边除以

- 840

\frac{- 840 cos ( x )}{- 840} = \frac{591}{- 840}

化简

\frac{- 840 cos ( x )}{- 840} = \frac{591}{- 840}

化简

\frac{- 840 cos ( x )}{- 840} : cos (x)

\frac{- 840 cos ( x )}{- 840}

使用分式法则:

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

= \frac{840 cos ( x )}{840}

数字相除:

\frac{840}{840} = 1

= cos (x)

化简

\frac{591}{- 840} : - \frac{197}{280}

\frac{591}{- 840}

使用分式法则:

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

= - \frac{591}{840}

约分:

3

= - \frac{197}{280}

cos (x) = - \frac{197}{280}

cos (x) = - \frac{197}{280}

cos (x) = - \frac{197}{280}

使用反三角函数性质

cos (x) = - \frac{197}{280}

cos (x) = - \frac{197}{280}

的通解

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

x = arccos (- \frac{197}{280}) + 2 πn, x = - arccos (- \frac{197}{280}) + 2 πn

x = arccos (- \frac{197}{280}) + 2 πn, x = - arccos (- \frac{197}{280}) + 2 πn

以小数形式表示解

x = 2.35120 \dots + 2 πn, x = - 2.35120 \dots + 2 πn

作图

流行的例子

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