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受欢迎的三角函数 >

144=100+6.93^2-2106.93*cos(x)

解答

144 = 100 + 6.9 3^{2} - 2 \cdot 10 \cdot 6.93 \cdot cos (x)

解答

x = 1.54175 \dots + 2 πn, x = 2 π - 1.54175 \dots + 2 πn

+1

度数

x = 88.33591 \dots^{\circ} + 36 0^{\circ} n, x = 271.66408 \dots^{\circ} + 36 0^{\circ} n

求解步骤

144 = 100 + 6.9 3^{2} - 2 \cdot 10 \cdot 6.93 cos (x)

交换两边

100 + 6.9 3^{2} - 2 \cdot 10 \cdot 6.93 cos (x) = 144

数字相乘:

2 \cdot 10 \cdot 6.93 = 138.6

100 + 6.9 3^{2} - 138.6 cos (x) = 144

6.9 3^{2} = 48.0249

100 + 48.0249 - 138.6 cos (x) = 144

数字相加:

100 + 48.0249 = 148.0249

- 138.6 cos (x) + 148.0249 = 144

将

148.0249

到右边

- 138.6 cos (x) + 148.0249 = 144

两边减去

148.0249

- 138.6 cos (x) + 148.0249 - 148.0249 = 144 - 148.0249

化简

- 138.6 cos (x) = - 4.0249

- 138.6 cos (x) = - 4.0249

两边除以

- 138.6

- 138.6 cos (x) = - 4.0249

两边除以

- 138.6

\frac{- 138.6 cos ( x )}{- 138.6} = \frac{- 4.0249}{- 138.6}

化简

cos (x) = \frac{4.0249}{138.6}

cos (x) = \frac{4.0249}{138.6}

使用反三角函数性质

cos (x) = \frac{4.0249}{138.6}

cos (x) = \frac{4.0249}{138.6}

的通解

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

x = arccos (\frac{4.0249}{138.6}) + 2 πn, x = 2 π - arccos (\frac{4.0249}{138.6}) + 2 πn

x = arccos (\frac{4.0249}{138.6}) + 2 πn, x = 2 π - arccos (\frac{4.0249}{138.6}) + 2 πn

以小数形式表示解

x = 1.54175 \dots + 2 πn, x = 2 π - 1.54175 \dots + 2 πn

作图

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