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受欢迎的三角函数 >

23cos(x)=-17-cos(x)

解答

23 cos (x) = - 17 - cos (x)

解答

x = 2.35793 \dots + 2 πn, x = - 2.35793 \dots + 2 πn

+1

度数

x = 135.09947 \dots^{\circ} + 36 0^{\circ} n, x = - 135.09947 \dots^{\circ} + 36 0^{\circ} n

求解步骤

23 cos (x) = - 17 - cos (x)

用替代法求解

23 cos (x) = - 17 - cos (x)

令

: cos (x) = u

23 u = - 17 - u

23 u = - 17 - u : u = - \frac{17}{24}

23 u = - 17 - u

将

u

para o lado esquerdo

23 u = - 17 - u

两边加上

u

23 u + u = - 17 - u + u

化简

24 u = - 17

24 u = - 17

两边除以

24

24 u = - 17

两边除以

24

\frac{24 u}{24} = \frac{- 17}{24}

化简

u = - \frac{17}{24}

u = - \frac{17}{24}

u = cos (x)

代回

cos (x) = - \frac{17}{24}

cos (x) = - \frac{17}{24}

cos (x) = - \frac{17}{24} : x = arccos (- \frac{17}{24}) + 2 πn, x = - arccos (- \frac{17}{24}) + 2 πn

cos (x) = - \frac{17}{24}

使用反三角函数性质

cos (x) = - \frac{17}{24}

cos (x) = - \frac{17}{24}

的通解

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

x = arccos (- \frac{17}{24}) + 2 πn, x = - arccos (- \frac{17}{24}) + 2 πn

x = arccos (- \frac{17}{24}) + 2 πn, x = - arccos (- \frac{17}{24}) + 2 πn

合并所有解

x = arccos (- \frac{17}{24}) + 2 πn, x = - arccos (- \frac{17}{24}) + 2 πn

以小数形式表示解

x = 2.35793 \dots + 2 πn, x = - 2.35793 \dots + 2 πn

作图

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