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受欢迎的三角函数 >

10cos(c)+1=cos(c)-1

解答

10 cos (c) + 1 = cos (c) - 1

解答

c = 1.79488 \dots + 2 πn, c = - 1.79488 \dots + 2 πn

+1

度数

c = 102.83958 \dots^{\circ} + 36 0^{\circ} n, c = - 102.83958 \dots^{\circ} + 36 0^{\circ} n

求解步骤

10 cos (c) + 1 = cos (c) - 1

用替代法求解

10 cos (c) + 1 = cos (c) - 1

令

: cos (c) = u

10 u + 1 = u - 1

10 u + 1 = u - 1 : u = - \frac{2}{9}

10 u + 1 = u - 1

将

1

到右边

10 u + 1 = u - 1

两边减去

1

10 u + 1 - 1 = u - 1 - 1

化简

10 u = u - 2

10 u = u - 2

将

u

para o lado esquerdo

10 u = u - 2

两边减去

u

10 u - u = u - 2 - u

化简

9 u = - 2

9 u = - 2

两边除以

9

9 u = - 2

两边除以

9

\frac{9 u}{9} = \frac{- 2}{9}

化简

u = - \frac{2}{9}

u = - \frac{2}{9}

u = cos (c)

代回

cos (c) = - \frac{2}{9}

cos (c) = - \frac{2}{9}

cos (c) = - \frac{2}{9} : c = arccos (- \frac{2}{9}) + 2 πn, c = - arccos (- \frac{2}{9}) + 2 πn

cos (c) = - \frac{2}{9}

使用反三角函数性质

cos (c) = - \frac{2}{9}

cos (c) = - \frac{2}{9}

的通解

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

c = arccos (- \frac{2}{9}) + 2 πn, c = - arccos (- \frac{2}{9}) + 2 πn

c = arccos (- \frac{2}{9}) + 2 πn, c = - arccos (- \frac{2}{9}) + 2 πn

合并所有解

c = arccos (- \frac{2}{9}) + 2 πn, c = - arccos (- \frac{2}{9}) + 2 πn

以小数形式表示解

c = 1.79488 \dots + 2 πn, c = - 1.79488 \dots + 2 πn

作图

流行的例子

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