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受欢迎的三角函数 >

4674.04= 5/(3cos(x))*2804.42

解答

4674.04 = \frac{5}{3 cos ( x )} \cdot 2804.42

解答

x = 0.00168 \dots + 2 πn, x = 2 π - 0.00168 \dots + 2 πn

+1

度数

x = 0.09677 \dots^{\circ} + 36 0^{\circ} n, x = 359.90322 \dots^{\circ} + 36 0^{\circ} n

求解步骤

4674.04 = \frac{5}{3 cos ( x )} \cdot 2804.42

交换两边

\frac{5}{3 cos ( x )} \cdot 2804.42 = 4674.04

在两边乘以

100

\frac{5}{3 cos ( x )} \cdot 2804.42 = 4674.04

To eliminate decimal points, multiply by 10 for every digit after the decimal pointThere are

2

digits to the right of the decimal point, therefore multiply by

100

\frac{5}{3 cos ( x )} \cdot 2804.42 \cdot 100 = 4674.04 \cdot 100

整理后得

\frac{1402210}{3 cos ( x )} = 467404

\frac{1402210}{3 cos ( x )} = 467404

在两边乘以

cos (x)

\frac{1402210}{3 cos ( x )} = 467404

在两边乘以

cos (x)

\frac{1402210}{3 cos ( x )} cos (x) = 467404 cos (x)

化简

\frac{1402210}{3} = 467404 cos (x)

\frac{1402210}{3} = 467404 cos (x)

交换两边

467404 cos (x) = \frac{1402210}{3}

两边除以

467404

467404 cos (x) = \frac{1402210}{3}

两边除以

467404

\frac{467404 cos ( x )}{467404} = \frac{\frac{1402210}{3}}{467404}

化简

\frac{467404 cos ( x )}{467404} = \frac{\frac{1402210}{3}}{467404}

化简

\frac{467404 cos ( x )}{467404} : cos (x)

\frac{467404 cos ( x )}{467404}

数字相除:

\frac{467404}{467404} = 1

= cos (x)

化简

\frac{\frac{1402210}{3}}{467404} : \frac{701105}{701106}

\frac{\frac{1402210}{3}}{467404}

使用分式法则:

\frac{\frac{b}{c}}{a} = \frac{b}{c \cdot a}

= \frac{1402210}{3 \cdot 467404}

数字相乘:

3 \cdot 467404 = 1402212

= \frac{1402210}{1402212}

约分:

2

= \frac{701105}{701106}

cos (x) = \frac{701105}{701106}

cos (x) = \frac{701105}{701106}

cos (x) = \frac{701105}{701106}

验证解

找到无定义的点（奇点）:

cos (x) = 0

取

\frac{5}{3 cos ( x )} 2804.42

的分母，令其等于零

解

3 cos (x) = 0 : cos (x) = 0

3 cos (x) = 0

两边除以

3

3 cos (x) = 0

两边除以

3

\frac{3 cos ( x )}{3} = \frac{0}{3}

化简

cos (x) = 0

cos (x) = 0

以下点无定义

cos (x) = 0

将不在定义域的点与解相综合:

cos (x) = \frac{701105}{701106}

使用反三角函数性质

cos (x) = \frac{701105}{701106}

cos (x) = \frac{701105}{701106}

的通解

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

x = arccos (\frac{701105}{701106}) + 2 πn, x = 2 π - arccos (\frac{701105}{701106}) + 2 πn

x = arccos (\frac{701105}{701106}) + 2 πn, x = 2 π - arccos (\frac{701105}{701106}) + 2 πn

以小数形式表示解

x = 0.00168 \dots + 2 πn, x = 2 π - 0.00168 \dots + 2 πn

作图

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