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受欢迎的三角函数 >

2=3sin(|5x|)+1

解答

2 = 3 sin (∣ 5 x ∣) + 1

解答

x \in R 无解

求解步骤

2 = 3 sin (∣ 5 x ∣) + 1

交换两边

3 sin (∣ 5 x ∣) + 1 = 2

将

1

到右边

3 sin (∣ 5 x ∣) + 1 = 2

两边减去

1

3 sin (∣ 5 x ∣) + 1 - 1 = 2 - 1

化简

3 sin (∣ 5 x ∣) = 1

3 sin (∣ 5 x ∣) = 1

两边除以

3

3 sin (∣ 5 x ∣) = 1

两边除以

3

\frac{3 sin ( ∣ 5 x ∣ )}{3} = \frac{1}{3}

化简

sin (∣ 5 x ∣) = \frac{1}{3}

sin (∣ 5 x ∣) = \frac{1}{3}

使用反三角函数性质

sin (∣ 5 x ∣) = \frac{1}{3}

sin (∣ 5 x ∣) = \frac{1}{3}

的通解

sin (x) = a \Rightarrow x = arcsin (a) + 2 πn, x = π - arcsin (a) + 2 πn

∣ 5 x ∣ = arcsin (\frac{1}{3}) + 2 πn, ∣ 5 x ∣ = π - arcsin (\frac{1}{3}) + 2 πn

∣ 5 x ∣ = arcsin (\frac{1}{3}) + 2 πn, ∣ 5 x ∣ = π - arcsin (\frac{1}{3}) + 2 πn

解

∣ 5 x ∣ = arcsin (\frac{1}{3}) + 2 πn :

无解

∣ 5 x ∣ = arcsin (\frac{1}{3}) + 2 πn

使用绝对值运算法则: 若

∣ u ∣ = a, a > 0

，则

u = a

or

u = - a

5 x = - (arcsin (\frac{1}{3}) + 2 πn) or 5 x = arcsin (\frac{1}{3}) + 2 πn

5 x = - (arcsin (\frac{1}{3}) + 2 πn) or 5 x = arcsin (\frac{1}{3}) + 2 πn

5 x = - (arcsin (\frac{1}{3}) + 2 πn) or 5 x = arcsin (\frac{1}{3}) + 2 πn

5 x = - (arcsin (\frac{1}{3}) + 2 πn) : x = - \frac{arcsin ( \frac{1}{3} ) + 2 πn}{5}

5 x = - (arcsin (\frac{1}{3}) + 2 πn)

两边除以

5

5 x = - (arcsin (\frac{1}{3}) + 2 πn)

两边除以

5

\frac{5 x}{5} = \frac{- ( arcsin ( \frac{1}{3} ) + 2 πn )}{5}

化简

\frac{5 x}{5} = \frac{- ( arcsin ( \frac{1}{3} ) + 2 πn )}{5}

化简

\frac{5 x}{5} : x

\frac{5 x}{5}

数字相除:

\frac{5}{5} = 1

= x

化简

\frac{- ( arcsin ( \frac{1}{3} ) + 2 πn )}{5} : - \frac{arcsin ( \frac{1}{3} ) + 2 πn}{5}

\frac{- ( arcsin ( \frac{1}{3} ) + 2 πn )}{5}

使用分式法则:

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

= - \frac{( arcsin ( \frac{1}{3} ) + 2 πn )}{5}

去除括号:

(a) = a

= - \frac{arcsin ( \frac{1}{3} ) + 2 πn}{5}

x = - \frac{arcsin ( \frac{1}{3} ) + 2 πn}{5}

x = - \frac{arcsin ( \frac{1}{3} ) + 2 πn}{5}

x = - \frac{arcsin ( \frac{1}{3} ) + 2 πn}{5}

5 x = arcsin (\frac{1}{3}) + 2 πn : x = \frac{arcsin ( \frac{1}{3} ) + 2 πn}{5}

5 x = arcsin (\frac{1}{3}) + 2 πn

两边除以

5

5 x = arcsin (\frac{1}{3}) + 2 πn

两边除以

5

\frac{5 x}{5} = \frac{arcsin ( \frac{1}{3} )}{5} + \frac{2 πn}{5}

化简

\frac{5 x}{5} = \frac{arcsin ( \frac{1}{3} )}{5} + \frac{2 πn}{5}

化简

\frac{5 x}{5} : x

\frac{5 x}{5}

数字相除:

\frac{5}{5} = 1

= x

化简

\frac{arcsin ( \frac{1}{3} )}{5} + \frac{2 πn}{5} : \frac{arcsin ( \frac{1}{3} ) + 2 πn}{5}

\frac{arcsin ( \frac{1}{3} )}{5} + \frac{2 πn}{5}

使用法则

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

= \frac{arcsin ( \frac{1}{3} ) + 2 πn}{5}

x = \frac{arcsin ( \frac{1}{3} ) + 2 πn}{5}

x = \frac{arcsin ( \frac{1}{3} ) + 2 πn}{5}

x = \frac{arcsin ( \frac{1}{3} ) + 2 πn}{5}

合并解:

无解 or 无解

无解 or 无解

x \in R 无解

解

∣ 5 x ∣ = π - arcsin (\frac{1}{3}) + 2 πn :

无解

∣ 5 x ∣ = π - arcsin (\frac{1}{3}) + 2 πn

使用绝对值运算法则: 若

∣ u ∣ = a, a > 0

，则

u = a

or

u = - a

5 x = - (π - arcsin (\frac{1}{3}) + 2 πn) or 5 x = π - arcsin (\frac{1}{3}) + 2 πn

5 x = - (π - arcsin (\frac{1}{3}) + 2 πn) or 5 x = π - arcsin (\frac{1}{3}) + 2 πn

5 x = - (π - arcsin (\frac{1}{3}) + 2 πn) or 5 x = π - arcsin (\frac{1}{3}) + 2 πn

5 x = - (π - arcsin (\frac{1}{3}) + 2 πn) : x = - \frac{π - arcsin ( \frac{1}{3} ) + 2 πn}{5}

5 x = - (π - arcsin (\frac{1}{3}) + 2 πn)

两边除以

5

5 x = - (π - arcsin (\frac{1}{3}) + 2 πn)

两边除以

5

\frac{5 x}{5} = \frac{- ( π - arcsin ( \frac{1}{3} ) + 2 πn )}{5}

化简

\frac{5 x}{5} = \frac{- ( π - arcsin ( \frac{1}{3} ) + 2 πn )}{5}

化简

\frac{5 x}{5} : x

\frac{5 x}{5}

数字相除:

\frac{5}{5} = 1

= x

化简

\frac{- ( π - arcsin ( \frac{1}{3} ) + 2 πn )}{5} : - \frac{π - arcsin ( \frac{1}{3} ) + 2 πn}{5}

\frac{- ( π - arcsin ( \frac{1}{3} ) + 2 πn )}{5}

使用分式法则:

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

= - \frac{( π - arcsin ( \frac{1}{3} ) + 2 πn )}{5}

去除括号:

(a) = a

= - \frac{π - arcsin ( \frac{1}{3} ) + 2 πn}{5}

x = - \frac{π - arcsin ( \frac{1}{3} ) + 2 πn}{5}

x = - \frac{π - arcsin ( \frac{1}{3} ) + 2 πn}{5}

x = - \frac{π - arcsin ( \frac{1}{3} ) + 2 πn}{5}

5 x = π - arcsin (\frac{1}{3}) + 2 πn : x = \frac{π - arcsin ( \frac{1}{3} ) + 2 πn}{5}

5 x = π - arcsin (\frac{1}{3}) + 2 πn

两边除以

5

5 x = π - arcsin (\frac{1}{3}) + 2 πn

两边除以

5

\frac{5 x}{5} = \frac{π}{5} - \frac{arcsin ( \frac{1}{3} )}{5} + \frac{2 πn}{5}

化简

\frac{5 x}{5} = \frac{π}{5} - \frac{arcsin ( \frac{1}{3} )}{5} + \frac{2 πn}{5}

化简

\frac{5 x}{5} : x

\frac{5 x}{5}

数字相除:

\frac{5}{5} = 1

= x

化简

\frac{π}{5} - \frac{arcsin ( \frac{1}{3} )}{5} + \frac{2 πn}{5} : \frac{π - arcsin ( \frac{1}{3} ) + 2 πn}{5}

\frac{π}{5} - \frac{arcsin ( \frac{1}{3} )}{5} + \frac{2 πn}{5}

使用法则

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

= \frac{π - arcsin ( \frac{1}{3} ) + 2 πn}{5}

x = \frac{π - arcsin ( \frac{1}{3} ) + 2 πn}{5}

x = \frac{π - arcsin ( \frac{1}{3} ) + 2 πn}{5}

x = \frac{π - arcsin ( \frac{1}{3} ) + 2 πn}{5}

合并解:

无解 or 无解

无解 or 无解

x \in R 无解

x = 无解, x = 无解

因为方程对以下值无定义:

无解

x \in R 无解

作图

流行的例子

sin (θ) = - \frac{1}{3}

sin (θ) = - \frac{1}{4}

sin(θ)cos(θ)= 1/2

sin (θ) cos (θ) = \frac{1}{2}

cos(θ)=(-sqrt(3))/2

cos (θ) = \frac{- 3}{2}

sin(x)cos(x)=sin(2x)

sin (x) cos (x) = sin (2 x)