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受欢迎的三角函数 >

29cos(x)=-17-cos(x)

解答

29 cos (x) = - 17 - cos (x)

解答

x = 2.17325 \dots + 2 πn, x = - 2.17325 \dots + 2 πn

+1

度数

x = 124.51810 \dots^{\circ} + 36 0^{\circ} n, x = - 124.51810 \dots^{\circ} + 36 0^{\circ} n

求解步骤

29 cos (x) = - 17 - cos (x)

用替代法求解

29 cos (x) = - 17 - cos (x)

令

: cos (x) = u

29 u = - 17 - u

29 u = - 17 - u : u = - \frac{17}{30}

29 u = - 17 - u

将

u

para o lado esquerdo

29 u = - 17 - u

两边加上

u

29 u + u = - 17 - u + u

化简

30 u = - 17

30 u = - 17

两边除以

30

30 u = - 17

两边除以

30

\frac{30 u}{30} = \frac{- 17}{30}

化简

u = - \frac{17}{30}

u = - \frac{17}{30}

u = cos (x)

代回

cos (x) = - \frac{17}{30}

cos (x) = - \frac{17}{30}

cos (x) = - \frac{17}{30} : x = arccos (- \frac{17}{30}) + 2 πn, x = - arccos (- \frac{17}{30}) + 2 πn

cos (x) = - \frac{17}{30}

使用反三角函数性质

cos (x) = - \frac{17}{30}

cos (x) = - \frac{17}{30}

的通解

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

x = arccos (- \frac{17}{30}) + 2 πn, x = - arccos (- \frac{17}{30}) + 2 πn

x = arccos (- \frac{17}{30}) + 2 πn, x = - arccos (- \frac{17}{30}) + 2 πn

合并所有解

x = arccos (- \frac{17}{30}) + 2 πn, x = - arccos (- \frac{17}{30}) + 2 πn

以小数形式表示解

x = 2.17325 \dots + 2 πn, x = - 2.17325 \dots + 2 πn

作图

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