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受欢迎的三角函数 >

sin(40-x)=cos(3x)

解答

sin (4 0^{\circ} - x) = cos (3 x)

解答

x = \frac{648 0 ^{\circ} n + 90 0 ^{\circ}}{36}, x = - \frac{90 0 ^{\circ} + 648 0 ^{\circ} n}{72}

+1

弧度

x = \frac{5 π}{36} + \frac{36 π}{36} n, x = - \frac{5 π}{72} - \frac{36 π}{72} n

求解步骤

sin (4 0^{\circ} - x) = cos (3 x)

使用三角恒等式改写

sin (4 0^{\circ} - x) = cos (3 x)

利用以下特性:

cos (x) = sin (9 0^{\circ} - x)

sin (4 0^{\circ} - x) = sin (9 0^{\circ} - 3 x)

sin (4 0^{\circ} - x) = sin (9 0^{\circ} - 3 x)

使用反三角函数性质

sin (4 0^{\circ} - x) = sin (9 0^{\circ} - 3 x)

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

4 0^{\circ} - x = 9 0^{\circ} - 3 x + 36 0^{\circ} n, 4 0^{\circ} - x = 18 0^{\circ} - (9 0^{\circ} - 3 x) + 36 0^{\circ} n

4 0^{\circ} - x = 9 0^{\circ} - 3 x + 36 0^{\circ} n, 4 0^{\circ} - x = 18 0^{\circ} - (9 0^{\circ} - 3 x) + 36 0^{\circ} n

4 0^{\circ} - x = 9 0^{\circ} - 3 x + 36 0^{\circ} n : x = \frac{648 0 ^{\circ} n + 90 0 ^{\circ}}{36}

4 0^{\circ} - x = 9 0^{\circ} - 3 x + 36 0^{\circ} n

将

4 0^{\circ}

到右边

4 0^{\circ} - x = 9 0^{\circ} - 3 x + 36 0^{\circ} n

两边减去

4 0^{\circ}

4 0^{\circ} - x - 4 0^{\circ} = 9 0^{\circ} - 3 x + 36 0^{\circ} n - 4 0^{\circ}

化简

4 0^{\circ} - x - 4 0^{\circ} = 9 0^{\circ} - 3 x + 36 0^{\circ} n - 4 0^{\circ}

化简

4 0^{\circ} - x - 4 0^{\circ} : - x

4 0^{\circ} - x - 4 0^{\circ}

同类项相加:

4 0^{\circ} - 4 0^{\circ} = 0

= - x

化简

9 0^{\circ} - 3 x + 36 0^{\circ} n - 4 0^{\circ} : - 3 x + 36 0^{\circ} n + 5 0^{\circ}

9 0^{\circ} - 3 x + 36 0^{\circ} n - 4 0^{\circ}

对同类项分组

= - 3 x + 36 0^{\circ} n + 9 0^{\circ} - 4 0^{\circ}

2, 9

的最小公倍数:

18

2, 9

最小公倍数 (LCM)

2

质因数分解:

2

2

2

是质数，因此无法因数分解

= 2

9

质因数分解:

3 \cdot 3

9

9

除以

39 = 3 \cdot 3

= 3 \cdot 3

将每个因子乘以它在

2

或

9

中出现的最多次数

= 2 \cdot 3 \cdot 3

数字相乘:

2 \cdot 3 \cdot 3 = 18

= 18

根据最小公倍数调整分式

将每个分子乘以其分母转变为最小公倍数所要乘以的同一数值

18

对于

9 0^{\circ} :

将分母和分子乘以

9

9 0^{\circ} = \frac{18 0 ^{\circ} 9}{2 \cdot 9} = 9 0^{\circ}

对于

4 0^{\circ} :

将分母和分子乘以

2

4 0^{\circ} = \frac{36 0 ^{\circ} 2}{9 \cdot 2} = 4 0^{\circ}

= 9 0^{\circ} - 4 0^{\circ}

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{18 0 ^{\circ} 9 - 72 0 ^{\circ}}{18}

同类项相加:

162 0^{\circ} - 72 0^{\circ} = 90 0^{\circ}

= - 3 x + 36 0^{\circ} n + 5 0^{\circ}

- x = - 3 x + 36 0^{\circ} n + 5 0^{\circ}

- x = - 3 x + 36 0^{\circ} n + 5 0^{\circ}

- x = - 3 x + 36 0^{\circ} n + 5 0^{\circ}

将

3 x

para o lado esquerdo

- x = - 3 x + 36 0^{\circ} n + 5 0^{\circ}

两边加上

3 x

- x + 3 x = - 3 x + 36 0^{\circ} n + 5 0^{\circ} + 3 x

化简

2 x = 36 0^{\circ} n + 5 0^{\circ}

2 x = 36 0^{\circ} n + 5 0^{\circ}

两边除以

2

2 x = 36 0^{\circ} n + 5 0^{\circ}

两边除以

2

\frac{2 x}{2} = \frac{36 0 ^{\circ} n}{2} + \frac{5 0 ^{\circ}}{2}

化简

\frac{2 x}{2} = \frac{36 0 ^{\circ} n}{2} + \frac{5 0 ^{\circ}}{2}

化简

\frac{2 x}{2} : x

\frac{2 x}{2}

数字相除:

\frac{2}{2} = 1

= x

化简

\frac{36 0 ^{\circ} n}{2} + \frac{5 0 ^{\circ}}{2} : \frac{648 0 ^{\circ} n + 90 0 ^{\circ}}{36}

\frac{36 0 ^{\circ} n}{2} + \frac{5 0 ^{\circ}}{2}

使用法则

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

= \frac{36 0 ^{\circ} n + 5 0 ^{\circ}}{2}

化简

36 0^{\circ} n + 5 0^{\circ} : \frac{648 0 ^{\circ} n + 90 0 ^{\circ}}{18}

36 0^{\circ} n + 5 0^{\circ}

将项转换为分式:

36 0^{\circ} n = \frac{36 0 ^{\circ} n 18}{18}

= \frac{36 0 ^{\circ} n \cdot 18}{18} + 5 0^{\circ}

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{36 0 ^{\circ} n \cdot 18 + 90 0 ^{\circ}}{18}

数字相乘:

2 \cdot 18 = 36

= \frac{648 0 ^{\circ} n + 90 0 ^{\circ}}{18}

= \frac{\frac{648 0 ^{\circ} n + 90 0 ^{\circ}}{18}}{2}

使用分式法则:

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

= \frac{648 0 ^{\circ} n + 90 0 ^{\circ}}{18 \cdot 2}

数字相乘:

18 \cdot 2 = 36

= \frac{648 0 ^{\circ} n + 90 0 ^{\circ}}{36}

x = \frac{648 0 ^{\circ} n + 90 0 ^{\circ}}{36}

x = \frac{648 0 ^{\circ} n + 90 0 ^{\circ}}{36}

x = \frac{648 0 ^{\circ} n + 90 0 ^{\circ}}{36}

4 0^{\circ} - x = 18 0^{\circ} - (9 0^{\circ} - 3 x) + 36 0^{\circ} n : x = - \frac{90 0 ^{\circ} + 648 0 ^{\circ} n}{72}

4 0^{\circ} - x = 18 0^{\circ} - (9 0^{\circ} - 3 x) + 36 0^{\circ} n

展开

18 0^{\circ} - (9 0^{\circ} - 3 x) + 36 0^{\circ} n : 18 0^{\circ} - 9 0^{\circ} + 3 x + 36 0^{\circ} n

18 0^{\circ} - (9 0^{\circ} - 3 x) + 36 0^{\circ} n

- (9 0^{\circ} - 3 x) : - 9 0^{\circ} + 3 x

- (9 0^{\circ} - 3 x)

打开括号

= - (9 0^{\circ}) - (- 3 x)

使用加减运算法则

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

= - 9 0^{\circ} + 3 x

= 18 0^{\circ} - 9 0^{\circ} + 3 x + 36 0^{\circ} n

4 0^{\circ} - x = 18 0^{\circ} - 9 0^{\circ} + 3 x + 36 0^{\circ} n

将

4 0^{\circ}

到右边

4 0^{\circ} - x = 18 0^{\circ} - 9 0^{\circ} + 3 x + 36 0^{\circ} n

两边减去

4 0^{\circ}

4 0^{\circ} - x - 4 0^{\circ} = 18 0^{\circ} - 9 0^{\circ} + 3 x + 36 0^{\circ} n - 4 0^{\circ}

化简

4 0^{\circ} - x - 4 0^{\circ} = 18 0^{\circ} - 9 0^{\circ} + 3 x + 36 0^{\circ} n - 4 0^{\circ}

化简

4 0^{\circ} - x - 4 0^{\circ} : - x

4 0^{\circ} - x - 4 0^{\circ}

同类项相加:

4 0^{\circ} - 4 0^{\circ} = 0

= - x

化简

18 0^{\circ} - 9 0^{\circ} + 3 x + 36 0^{\circ} n - 4 0^{\circ} : 3 x + 18 0^{\circ} + 36 0^{\circ} n - 13 0^{\circ}

18 0^{\circ} - 9 0^{\circ} + 3 x + 36 0^{\circ} n - 4 0^{\circ}

对同类项分组

= 3 x + 18 0^{\circ} + 36 0^{\circ} n - 9 0^{\circ} - 4 0^{\circ}

2, 9

的最小公倍数:

18

2, 9

最小公倍数 (LCM)

2

质因数分解:

2

2

2

是质数，因此无法因数分解

= 2

9

质因数分解:

3 \cdot 3

9

9

除以

39 = 3 \cdot 3

= 3 \cdot 3

将每个因子乘以它在

2

或

9

中出现的最多次数

= 2 \cdot 3 \cdot 3

数字相乘:

2 \cdot 3 \cdot 3 = 18

= 18

根据最小公倍数调整分式

将每个分子乘以其分母转变为最小公倍数所要乘以的同一数值

18

对于

9 0^{\circ} :

将分母和分子乘以

9

9 0^{\circ} = \frac{18 0 ^{\circ} 9}{2 \cdot 9} = 9 0^{\circ}

对于

4 0^{\circ} :

将分母和分子乘以

2

4 0^{\circ} = \frac{36 0 ^{\circ} 2}{9 \cdot 2} = 4 0^{\circ}

= - 9 0^{\circ} - 4 0^{\circ}

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{- 18 0 ^{\circ} 9 - 72 0 ^{\circ}}{18}

同类项相加:

- 162 0^{\circ} - 72 0^{\circ} = - 234 0^{\circ}

= \frac{- 234 0 ^{\circ}}{18}

使用分式法则:

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

= 3 x + 18 0^{\circ} + 36 0^{\circ} n - 13 0^{\circ}

- x = 3 x + 18 0^{\circ} + 36 0^{\circ} n - 13 0^{\circ}

- x = 3 x + 18 0^{\circ} + 36 0^{\circ} n - 13 0^{\circ}

- x = 3 x + 18 0^{\circ} + 36 0^{\circ} n - 13 0^{\circ}

将

3 x

para o lado esquerdo

- x = 3 x + 18 0^{\circ} + 36 0^{\circ} n - 13 0^{\circ}

两边减去

3 x

- x - 3 x = 3 x + 18 0^{\circ} + 36 0^{\circ} n - 13 0^{\circ} - 3 x

化简

- 4 x = 18 0^{\circ} + 36 0^{\circ} n - 13 0^{\circ}

- 4 x = 18 0^{\circ} + 36 0^{\circ} n - 13 0^{\circ}

两边除以

- 4

- 4 x = 18 0^{\circ} + 36 0^{\circ} n - 13 0^{\circ}

两边除以

- 4

\frac{- 4 x}{- 4} = \frac{18 0 ^{\circ}}{- 4} + \frac{36 0 ^{\circ} n}{- 4} - \frac{13 0 ^{\circ}}{- 4}

化简

\frac{- 4 x}{- 4} = \frac{18 0 ^{\circ}}{- 4} + \frac{36 0 ^{\circ} n}{- 4} - \frac{13 0 ^{\circ}}{- 4}

化简

\frac{- 4 x}{- 4} : x

\frac{- 4 x}{- 4}

使用分式法则:

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

= \frac{4 x}{4}

数字相除:

\frac{4}{4} = 1

= x

化简

\frac{18 0 ^{\circ}}{- 4} + \frac{36 0 ^{\circ} n}{- 4} - \frac{13 0 ^{\circ}}{- 4} : - \frac{90 0 ^{\circ} + 648 0 ^{\circ} n}{72}

\frac{18 0 ^{\circ}}{- 4} + \frac{36 0 ^{\circ} n}{- 4} - \frac{13 0 ^{\circ}}{- 4}

使用法则

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

= \frac{18 0 ^{\circ} + 36 0 ^{\circ} n - 13 0 ^{\circ}}{- 4}

使用分式法则:

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

= - \frac{18 0 ^{\circ} + 36 0 ^{\circ} n - 13 0 ^{\circ}}{4}

化简

18 0^{\circ} + 36 0^{\circ} n - 13 0^{\circ} : \frac{90 0 ^{\circ} + 648 0 ^{\circ} n}{18}

18 0^{\circ} + 36 0^{\circ} n - 13 0^{\circ}

将项转换为分式:

18 0^{\circ} = 18 0^{\circ}, 36 0^{\circ} n = \frac{36 0 ^{\circ} n 18}{18}

= 18 0^{\circ} + \frac{36 0 ^{\circ} n \cdot 18}{18} - 13 0^{\circ}

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{18 0 ^{\circ} 18 + 36 0 ^{\circ} n \cdot 18 - 234 0 ^{\circ}}{18}

18 0^{\circ} 18 + 36 0^{\circ} n \cdot 18 - 234 0^{\circ} = 90 0^{\circ} + 648 0^{\circ} n

18 0^{\circ} 18 + 36 0^{\circ} n \cdot 18 - 234 0^{\circ}

同类项相加:

324 0^{\circ} - 234 0^{\circ} = 90 0^{\circ}

= 90 0^{\circ} + 2 \cdot 324 0^{\circ} n

数字相乘:

2 \cdot 18 = 36

= 90 0^{\circ} + 648 0^{\circ} n

= \frac{90 0 ^{\circ} + 648 0 ^{\circ} n}{18}

= - \frac{\frac{90 0 ^{\circ} + 648 0 ^{\circ} n}{18}}{4}

化简

\frac{\frac{90 0 ^{\circ} + 648 0 ^{\circ} n}{18}}{4} : \frac{90 0 ^{\circ} + 648 0 ^{\circ} n}{72}

\frac{\frac{90 0 ^{\circ} + 648 0 ^{\circ} n}{18}}{4}

使用分式法则:

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

= \frac{90 0 ^{\circ} + 648 0 ^{\circ} n}{18 \cdot 4}

数字相乘:

18 \cdot 4 = 72

= \frac{90 0 ^{\circ} + 648 0 ^{\circ} n}{72}

= - \frac{90 0 ^{\circ} + 648 0 ^{\circ} n}{72}

x = - \frac{90 0 ^{\circ} + 648 0 ^{\circ} n}{72}

x = - \frac{90 0 ^{\circ} + 648 0 ^{\circ} n}{72}

x = - \frac{90 0 ^{\circ} + 648 0 ^{\circ} n}{72}

x = \frac{648 0 ^{\circ} n + 90 0 ^{\circ}}{36}, x = - \frac{90 0 ^{\circ} + 648 0 ^{\circ} n}{72}

x = \frac{648 0 ^{\circ} n + 90 0 ^{\circ}}{36}, x = - \frac{90 0 ^{\circ} + 648 0 ^{\circ} n}{72}

作图

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