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受欢迎的三角函数 >

14928=(18177)/((1+0.387cos(x)))

解答

14928 = \frac{18177}{( 1 + 0.387 cos ( x ) )}

解答

x = 0.97352 \dots + 2 πn, x = 2 π - 0.97352 \dots + 2 πn

+1

度数

x = 55.77879 \dots^{\circ} + 36 0^{\circ} n, x = 304.22120 \dots^{\circ} + 36 0^{\circ} n

求解步骤

14928 = \frac{18177}{( 1 + 0.387 cos ( x ) )}

交换两边

\frac{18177}{1 + 0.387 cos ( x )} = 14928

在两边乘以

1 + 0.387 cos (x)

\frac{18177}{1 + 0.387 cos ( x )} = 14928

在两边乘以

1 + 0.387 cos (x)

\frac{18177}{1 + 0.387 cos ( x )} (1 + 0.387 cos (x)) = 14928 (1 + 0.387 cos (x))

化简

18177 = 14928 (1 + 0.387 cos (x))

18177 = 14928 (1 + 0.387 cos (x))

交换两边

14928 (1 + 0.387 cos (x)) = 18177

两边除以

14928

14928 (1 + 0.387 cos (x)) = 18177

两边除以

14928

\frac{14928 ( 1 + 0.387 cos ( x ) )}{14928} = \frac{18177}{14928}

化简

1 + 0.387 cos (x) = \frac{6059}{4976}

1 + 0.387 cos (x) = \frac{6059}{4976}

将

1

到右边

1 + 0.387 cos (x) = \frac{6059}{4976}

两边减去

1

1 + 0.387 cos (x) - 1 = \frac{6059}{4976} - 1

化简

1 + 0.387 cos (x) - 1 = \frac{6059}{4976} - 1

化简

1 + 0.387 cos (x) - 1 : 0.387 cos (x)

1 + 0.387 cos (x) - 1

同类项相加:

1 - 1 = 0

= 0.387 cos (x)

化简

\frac{6059}{4976} - 1 : \frac{1083}{4976}

\frac{6059}{4976} - 1

将项转换为分式:

1 = \frac{1 \cdot 4976}{4976}

= - \frac{1 \cdot 4976}{4976} + \frac{6059}{4976}

因为分母相等，所以合并分式:

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

= \frac{- 1 \cdot 4976 + 6059}{4976}

- 1 \cdot 4976 + 6059 = 1083

- 1 \cdot 4976 + 6059

数字相乘:

1 \cdot 4976 = 4976

= - 4976 + 6059

数字相加/相减:

- 4976 + 6059 = 1083

= 1083

= \frac{1083}{4976}

0.387 cos (x) = \frac{1083}{4976}

0.387 cos (x) = \frac{1083}{4976}

0.387 cos (x) = \frac{1083}{4976}

两边除以

0.387

0.387 cos (x) = \frac{1083}{4976}

两边除以

0.387

\frac{0.387 cos ( x )}{0.387} = \frac{\frac{1083}{4976}}{0.387}

化简

\frac{0.387 cos ( x )}{0.387} = \frac{\frac{1083}{4976}}{0.387}

化简

\frac{0.387 cos ( x )}{0.387} : cos (x)

\frac{0.387 cos ( x )}{0.387}

约分:

0.387

= cos (x)

化简

\frac{\frac{1083}{4976}}{0.387} : 0.56238 \dots

\frac{\frac{1083}{4976}}{0.387}

使用分式法则:

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

= \frac{1083}{4976 \cdot 0.387}

数字相乘:

4976 \cdot 0.387 = 1925.712

= \frac{1083}{1925.712}

数字相除:

\frac{1083}{1925.712} = 0.56238 \dots

= 0.56238 \dots

cos (x) = 0.56238 \dots

cos (x) = 0.56238 \dots

cos (x) = 0.56238 \dots

验证解

找到无定义的点（奇点）:

cos (x) = - \frac{1000}{387}

取

\frac{18177}{1 + 0.387 cos ( x )}

的分母，令其等于零

解

1 + 0.387 cos (x) = 0 : cos (x) = - \frac{1000}{387}

1 + 0.387 cos (x) = 0

在两边乘以

1000

1 + 0.387 cos (x) = 0

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

3

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

1000

1 \cdot 1000 + 0.387 cos (x) \cdot 1000 = 0 \cdot 1000

整理后得

1000 + 387 cos (x) = 0

1000 + 387 cos (x) = 0

将

1000

到右边

1000 + 387 cos (x) = 0

两边减去

1000

1000 + 387 cos (x) - 1000 = 0 - 1000

化简

387 cos (x) = - 1000

387 cos (x) = - 1000

两边除以

387

387 cos (x) = - 1000

两边除以

387

\frac{387 cos ( x )}{387} = \frac{- 1000}{387}

化简

cos (x) = - \frac{1000}{387}

cos (x) = - \frac{1000}{387}

以下点无定义

cos (x) = - \frac{1000}{387}

将不在定义域的点与解相综合:

cos (x) = 0.56238 \dots

使用反三角函数性质

cos (x) = 0.56238 \dots

cos (x) = 0.56238 \dots

的通解

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

x = arccos (0.56238 \dots) + 2 πn, x = 2 π - arccos (0.56238 \dots) + 2 πn

x = arccos (0.56238 \dots) + 2 πn, x = 2 π - arccos (0.56238 \dots) + 2 πn

以小数形式表示解

x = 0.97352 \dots + 2 πn, x = 2 π - 0.97352 \dots + 2 πn

作图

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