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受欢迎的三角函数 >

16=4+9-12cos(x)

解答

16 = 4 + 9 - 12 cos (x)

解答

x = 1.82347 \dots + 2 πn, x = - 1.82347 \dots + 2 πn

+1

度数

x = 104.47751 \dots^{\circ} + 36 0^{\circ} n, x = - 104.47751 \dots^{\circ} + 36 0^{\circ} n

求解步骤

16 = 4 + 9 - 12 cos (x)

交换两边

4 + 9 - 12 cos (x) = 16

数字相加:

4 + 9 = 13

- 12 cos (x) + 13 = 16

将

13

到右边

- 12 cos (x) + 13 = 16

两边减去

13

- 12 cos (x) + 13 - 13 = 16 - 13

化简

- 12 cos (x) = 3

- 12 cos (x) = 3

两边除以

- 12

- 12 cos (x) = 3

两边除以

- 12

\frac{- 12 cos ( x )}{- 12} = \frac{3}{- 12}

化简

\frac{- 12 cos ( x )}{- 12} = \frac{3}{- 12}

化简

\frac{- 12 cos ( x )}{- 12} : cos (x)

\frac{- 12 cos ( x )}{- 12}

使用分式法则:

\frac{- a}{- b} = \frac{a}{b}

= \frac{12 cos ( x )}{12}

数字相除:

\frac{12}{12} = 1

= cos (x)

化简

\frac{3}{- 12} : - \frac{1}{4}

\frac{3}{- 12}

使用分式法则:

\frac{a}{- b} = - \frac{a}{b}

= - \frac{3}{12}

约分:

3

= - \frac{1}{4}

cos (x) = - \frac{1}{4}

cos (x) = - \frac{1}{4}

cos (x) = - \frac{1}{4}

使用反三角函数性质

cos (x) = - \frac{1}{4}

cos (x) = - \frac{1}{4}

的通解

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

x = arccos (- \frac{1}{4}) + 2 πn, x = - arccos (- \frac{1}{4}) + 2 πn

x = arccos (- \frac{1}{4}) + 2 πn, x = - arccos (- \frac{1}{4}) + 2 πn

以小数形式表示解

x = 1.82347 \dots + 2 πn, x = - 1.82347 \dots + 2 πn

作图

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