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受欢迎的三角函数 >

15cos(x)-5=4cos(x)

解答

15 cos (x) - 5 = 4 cos (x)

解答

x = 1.09893 \dots + 2 πn, x = 2 π - 1.09893 \dots + 2 πn

+1

度数

x = 62.96430 \dots^{\circ} + 36 0^{\circ} n, x = 297.03569 \dots^{\circ} + 36 0^{\circ} n

求解步骤

15 cos (x) - 5 = 4 cos (x)

用替代法求解

15 cos (x) - 5 = 4 cos (x)

令

: cos (x) = u

15 u - 5 = 4 u

15 u - 5 = 4 u : u = \frac{5}{11}

15 u - 5 = 4 u

将

5

到右边

15 u - 5 = 4 u

两边加上

5

15 u - 5 + 5 = 4 u + 5

化简

15 u = 4 u + 5

15 u = 4 u + 5

将

4 u

para o lado esquerdo

15 u = 4 u + 5

两边减去

4 u

15 u - 4 u = 4 u + 5 - 4 u

化简

11 u = 5

11 u = 5

两边除以

11

11 u = 5

两边除以

11

\frac{11 u}{11} = \frac{5}{11}

化简

u = \frac{5}{11}

u = \frac{5}{11}

u = cos (x)

代回

cos (x) = \frac{5}{11}

cos (x) = \frac{5}{11}

cos (x) = \frac{5}{11} : x = arccos (\frac{5}{11}) + 2 πn, x = 2 π - arccos (\frac{5}{11}) + 2 πn

cos (x) = \frac{5}{11}

使用反三角函数性质

cos (x) = \frac{5}{11}

cos (x) = \frac{5}{11}

的通解

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

x = arccos (\frac{5}{11}) + 2 πn, x = 2 π - arccos (\frac{5}{11}) + 2 πn

x = arccos (\frac{5}{11}) + 2 πn, x = 2 π - arccos (\frac{5}{11}) + 2 πn

合并所有解

x = arccos (\frac{5}{11}) + 2 πn, x = 2 π - arccos (\frac{5}{11}) + 2 πn

以小数形式表示解

x = 1.09893 \dots + 2 πn, x = 2 π - 1.09893 \dots + 2 πn

作图

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