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受欢迎的三角函数 >

sin(2x-0.35)=cos(3x)

解答

sin (2 x - 0.35) = cos (3 x)

解答

x = \frac{0.35 + \frac{π}{2} + 6.28318 \dots n}{5}, x = - 0.35 - 6.28318 \dots n - \frac{π}{2}

+1

度数

x = 22.01070 \dots^{\circ} + 7 2^{\circ} n, x = - 110.05352 \dots^{\circ} - 36 0^{\circ} n

求解步骤

sin (2 x - 0.35) = cos (3 x)

使用三角恒等式改写

sin (2 x - 0.35) = cos (3 x)

利用以下特性:

cos (x) = sin (\frac{π}{2} - x)

sin (2 x - 0.35) = sin (\frac{π}{2} - 3 x)

sin (2 x - 0.35) = sin (\frac{π}{2} - 3 x)

使用反三角函数性质

sin (2 x - 0.35) = sin (\frac{π}{2} - 3 x)

sin (x) = sin (y) \Rightarrow x = y + 2 π n, x = π - y + 2 π n

2 x - 0.35 = \frac{π}{2} - 3 x + 2 πn, 2 x - 0.35 = π - (\frac{π}{2} - 3 x) + 2 πn

2 x - 0.35 = \frac{π}{2} - 3 x + 2 πn, 2 x - 0.35 = π - (\frac{π}{2} - 3 x) + 2 πn

2 x - 0.35 = \frac{π}{2} - 3 x + 2 πn : x = \frac{0.35 + \frac{π}{2} + 6.28318 \dots n}{5}

2 x - 0.35 = \frac{π}{2} - 3 x + 2 πn

将

0.35

到右边

2 x - 0.35 = \frac{π}{2} - 3 x + 2 πn

两边加上

0.35

2 x - 0.35 + 0.35 = \frac{π}{2} - 3 x + 2 πn + 0.35

化简

2 x - 0.35 + 0.35 = \frac{π}{2} - 3 x + 2 πn + 0.35

化简

2 x - 0.35 + 0.35 : 2 x

2 x - 0.35 + 0.35

同类项相加:

- 0.35 + 0.35 = 0

= 2 x

化简

\frac{π}{2} - 3 x + 2 πn + 0.35 : \frac{π}{2} - 3 x + 6.28318 \dots n + 0.35

\frac{π}{2} - 3 x + 2 πn + 0.35

数字相乘:

2 \cdot 3.14159 \dots = 6.28318 \dots

= \frac{π}{2} - 3 x + 6.28318 \dots n + 0.35

2 x = \frac{π}{2} - 3 x + 6.28318 \dots n + 0.35

2 x = \frac{π}{2} - 3 x + 6.28318 \dots n + 0.35

2 x = \frac{π}{2} - 3 x + 6.28318 \dots n + 0.35

将

3 x

para o lado esquerdo

2 x = \frac{π}{2} - 3 x + 6.28318 \dots n + 0.35

两边加上

3 x

2 x + 3 x = \frac{π}{2} - 3 x + 6.28318 \dots n + 0.35 + 3 x

化简

5 x = \frac{π}{2} + 6.28318 \dots n + 0.35

5 x = \frac{π}{2} + 6.28318 \dots n + 0.35

两边除以

5

5 x = \frac{π}{2} + 6.28318 \dots n + 0.35

两边除以

5

\frac{5 x}{5} = \frac{\frac{π}{2}}{5} + \frac{6.28318 \dots n}{5} + \frac{0.35}{5}

化简

\frac{5 x}{5} = \frac{\frac{π}{2}}{5} + \frac{6.28318 \dots n}{5} + \frac{0.35}{5}

化简

\frac{5 x}{5} : x

\frac{5 x}{5}

数字相除:

\frac{5}{5} = 1

= x

化简

\frac{\frac{π}{2}}{5} + \frac{6.28318 \dots n}{5} + \frac{0.35}{5} : \frac{0.35 + \frac{π}{2} + 6.28318 \dots n}{5}

\frac{\frac{π}{2}}{5} + \frac{6.28318 \dots n}{5} + \frac{0.35}{5}

对同类项分组

= \frac{0.35}{5} + \frac{\frac{π}{2}}{5} + \frac{6.28318 \dots n}{5}

使用法则

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

= \frac{0.35 + \frac{π}{2} + 6.28318 \dots n}{5}

x = \frac{0.35 + \frac{π}{2} + 6.28318 \dots n}{5}

x = \frac{0.35 + \frac{π}{2} + 6.28318 \dots n}{5}

x = \frac{0.35 + \frac{π}{2} + 6.28318 \dots n}{5}

2 x - 0.35 = π - (\frac{π}{2} - 3 x) + 2 πn : x = - 0.35 - 6.28318 \dots n - \frac{π}{2}

2 x - 0.35 = π - (\frac{π}{2} - 3 x) + 2 πn

展开

π - (\frac{π}{2} - 3 x) + 2 πn : π - \frac{π}{2} + 3 x + 2 πn

π - (\frac{π}{2} - 3 x) + 2 πn

- (\frac{π}{2} - 3 x) : - \frac{π}{2} + 3 x

- (\frac{π}{2} - 3 x)

打开括号

= - (\frac{π}{2}) - (- 3 x)

使用加减运算法则

- (- a) = a, - (a) = - a

= - \frac{π}{2} + 3 x

= π - \frac{π}{2} + 3 x + 2 πn

2 x - 0.35 = π - \frac{π}{2} + 3 x + 2 πn

将

0.35

到右边

2 x - 0.35 = π - \frac{π}{2} + 3 x + 2 πn

两边加上

0.35

2 x - 0.35 + 0.35 = π - \frac{π}{2} + 3 x + 2 πn + 0.35

化简

2 x - 0.35 + 0.35 = π - \frac{π}{2} + 3 x + 2 πn + 0.35

化简

2 x - 0.35 + 0.35 : 2 x

2 x - 0.35 + 0.35

同类项相加:

- 0.35 + 0.35 = 0

= 2 x

化简

π - \frac{π}{2} + 3 x + 2 πn + 0.35 : π - \frac{π}{2} + 3 x + 6.28318 \dots n + 0.35

π - \frac{π}{2} + 3 x + 2 πn + 0.35

数字相乘:

2 \cdot 3.14159 \dots = 6.28318 \dots

= π - \frac{π}{2} + 3 x + 6.28318 \dots n + 0.35

2 x = π - \frac{π}{2} + 3 x + 6.28318 \dots n + 0.35

2 x = π - \frac{π}{2} + 3 x + 6.28318 \dots n + 0.35

2 x = π - \frac{π}{2} + 3 x + 6.28318 \dots n + 0.35

将

3 x

para o lado esquerdo

2 x = π - \frac{π}{2} + 3 x + 6.28318 \dots n + 0.35

两边减去

3 x

2 x - 3 x = π - \frac{π}{2} + 3 x + 6.28318 \dots n + 0.35 - 3 x

化简

- x = π - \frac{π}{2} + 6.28318 \dots n + 0.35

- x = π - \frac{π}{2} + 6.28318 \dots n + 0.35

两边除以

- 1

- x = π - \frac{π}{2} + 6.28318 \dots n + 0.35

两边除以

- 1

\frac{- x}{- 1} = \frac{π}{- 1} - \frac{\frac{π}{2}}{- 1} + \frac{6.28318 \dots n}{- 1} + \frac{0.35}{- 1}

化简

\frac{- x}{- 1} = \frac{π}{- 1} - \frac{\frac{π}{2}}{- 1} + \frac{6.28318 \dots n}{- 1} + \frac{0.35}{- 1}

化简

\frac{- x}{- 1} : x

\frac{- x}{- 1}

使用分式法则:

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

= \frac{x}{1}

使用法则

\frac{a}{1} = a

= x

化简

\frac{π}{- 1} - \frac{\frac{π}{2}}{- 1} + \frac{6.28318 \dots n}{- 1} + \frac{0.35}{- 1} : - 0.35 - 6.28318 \dots n - \frac{π}{2}

\frac{π}{- 1} - \frac{\frac{π}{2}}{- 1} + \frac{6.28318 \dots n}{- 1} + \frac{0.35}{- 1}

对同类项分组

= \frac{π}{- 1} + \frac{0.35}{- 1} - \frac{\frac{π}{2}}{- 1} + \frac{6.28318 \dots n}{- 1}

使用法则

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

= \frac{π + 0.35 - \frac{π}{2} + 6.28318 \dots n}{- 1}

使用分式法则:

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

= - \frac{π + 0.35 - \frac{π}{2} + 6.28318 \dots n}{1}

化简

π + 0.35 - \frac{π}{2} + 6.28318 \dots n : 0.35 + 6.28318 \dots n + \frac{π}{2}

π + 0.35 - \frac{π}{2} + 6.28318 \dots n

将项转换为分式:

π = \frac{π 2}{2}

= \frac{π 2}{2} - \frac{π}{2}

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{π 2 - π}{2}

同类项相加:

2 π - π = π

= \frac{π}{2}

= - \frac{6.28318 \dots n + 0.35 + \frac{π}{2}}{1}

使用分式法则:

\frac{a}{1} = a

\frac{0.35 + 6.28318 \dots n + \frac{π}{2}}{1} = 0.35 + 6.28318 \dots n + \frac{π}{2}

= - (0.35 + 6.28318 \dots n + \frac{π}{2})

打开括号

= - (0.35) - (6.28318 \dots n) - (\frac{π}{2})

使用加减运算法则

+ (- a) = - a

= - 0.35 - 6.28318 \dots n - \frac{π}{2}

x = - 0.35 - 6.28318 \dots n - \frac{π}{2}

x = - 0.35 - 6.28318 \dots n - \frac{π}{2}

x = - 0.35 - 6.28318 \dots n - \frac{π}{2}

x = \frac{0.35 + \frac{π}{2} + 6.28318 \dots n}{5}, x = - 0.35 - 6.28318 \dots n - \frac{π}{2}

x = \frac{0.35 + \frac{π}{2} + 6.28318 \dots n}{5}, x = - 0.35 - 6.28318 \dots n - \frac{π}{2}

作图

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