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受欢迎的三角函数 >

cos(2x)=sin(70+x)

解答

cos (2 x) = sin (7 0^{\circ} + x)

解答

x = \frac{324 0 ^{\circ} n + 18 0 ^{\circ}}{27}, x = - \frac{18 0 ^{\circ} + 324 0 ^{\circ} n}{9}

+1

弧度

x = \frac{π}{27} + \frac{18 π}{27} n, x = - \frac{π}{9} - \frac{18 π}{9} n

求解步骤

cos (2 x) = sin (7 0^{\circ} + x)

使用三角恒等式改写

cos (2 x) = sin (7 0^{\circ} + x)

利用以下特性:

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

cos (2 x) = sin (9 0^{\circ} - 2 x)

cos (2 x) = sin (9 0^{\circ} - 2 x)

使用反三角函数性质

cos (2 x) = sin (9 0^{\circ} - 2 x)

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

7 0^{\circ} + x = 9 0^{\circ} - 2 x + 36 0^{\circ} n, 7 0^{\circ} + x = 18 0^{\circ} - (9 0^{\circ} - 2 x) + 36 0^{\circ} n

7 0^{\circ} + x = 9 0^{\circ} - 2 x + 36 0^{\circ} n, 7 0^{\circ} + x = 18 0^{\circ} - (9 0^{\circ} - 2 x) + 36 0^{\circ} n

7 0^{\circ} + x = 9 0^{\circ} - 2 x + 36 0^{\circ} n : x = \frac{324 0 ^{\circ} n + 18 0 ^{\circ}}{27}

7 0^{\circ} + x = 9 0^{\circ} - 2 x + 36 0^{\circ} n

将

7 0^{\circ}

到右边

7 0^{\circ} + x = 9 0^{\circ} - 2 x + 36 0^{\circ} n

两边减去

7 0^{\circ}

7 0^{\circ} + x - 7 0^{\circ} = 9 0^{\circ} - 2 x + 36 0^{\circ} n - 7 0^{\circ}

化简

7 0^{\circ} + x - 7 0^{\circ} = 9 0^{\circ} - 2 x + 36 0^{\circ} n - 7 0^{\circ}

化简

7 0^{\circ} + x - 7 0^{\circ} : x

7 0^{\circ} + x - 7 0^{\circ}

同类项相加:

7 0^{\circ} - 7 0^{\circ} = 0

= x

化简

9 0^{\circ} - 2 x + 36 0^{\circ} n - 7 0^{\circ} : - 2 x + 36 0^{\circ} n + 2 0^{\circ}

9 0^{\circ} - 2 x + 36 0^{\circ} n - 7 0^{\circ}

对同类项分组

= - 2 x + 36 0^{\circ} n + 9 0^{\circ} - 7 0^{\circ}

2, 18

的最小公倍数:

18

2, 18

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

18

质因数分解:

2 \cdot 3 \cdot 3

18

18

除以

218 = 9 \cdot 2

= 2 \cdot 9

9

除以

39 = 3 \cdot 3

= 2 \cdot 3 \cdot 3

2, 3

都是质数，因此无法进一步因数分解

= 2 \cdot 3 \cdot 3

将每个因子乘以它在

2

或

18

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}

= 9 0^{\circ} - 7 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 - 126 0 ^{\circ}}{18}

同类项相加:

162 0^{\circ} - 126 0^{\circ} = 36 0^{\circ}

= 2 0^{\circ}

约分:

2

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

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

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

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

将

2 x

para o lado esquerdo

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

两边加上

2 x

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

化简

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

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

两边除以

3

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

两边除以

3

\frac{3 x}{3} = \frac{36 0 ^{\circ} n}{3} + \frac{2 0 ^{\circ}}{3}

化简

\frac{3 x}{3} = \frac{36 0 ^{\circ} n}{3} + \frac{2 0 ^{\circ}}{3}

化简

\frac{3 x}{3} : x

\frac{3 x}{3}

数字相除:

\frac{3}{3} = 1

= x

化简

\frac{36 0 ^{\circ} n}{3} + \frac{2 0 ^{\circ}}{3} : \frac{324 0 ^{\circ} n + 18 0 ^{\circ}}{27}

\frac{36 0 ^{\circ} n}{3} + \frac{2 0 ^{\circ}}{3}

使用法则

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

= \frac{36 0 ^{\circ} n + 2 0 ^{\circ}}{3}

化简

36 0^{\circ} n + 2 0^{\circ} : \frac{324 0 ^{\circ} n + 18 0 ^{\circ}}{9}

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

将项转换为分式:

36 0^{\circ} n = \frac{36 0 ^{\circ} n 9}{9}

= \frac{36 0 ^{\circ} n \cdot 9}{9} + 2 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 9 + 18 0 ^{\circ}}{9}

数字相乘:

2 \cdot 9 = 18

= \frac{324 0 ^{\circ} n + 18 0 ^{\circ}}{9}

= \frac{\frac{324 0 ^{\circ} n + 18 0 ^{\circ}}{9}}{3}

使用分式法则:

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

= \frac{324 0 ^{\circ} n + 18 0 ^{\circ}}{9 \cdot 3}

数字相乘:

9 \cdot 3 = 27

= \frac{324 0 ^{\circ} n + 18 0 ^{\circ}}{27}

x = \frac{324 0 ^{\circ} n + 18 0 ^{\circ}}{27}

x = \frac{324 0 ^{\circ} n + 18 0 ^{\circ}}{27}

x = \frac{324 0 ^{\circ} n + 18 0 ^{\circ}}{27}

7 0^{\circ} + x = 18 0^{\circ} - (9 0^{\circ} - 2 x) + 36 0^{\circ} n : x = - \frac{18 0 ^{\circ} + 324 0 ^{\circ} n}{9}

7 0^{\circ} + x = 18 0^{\circ} - (9 0^{\circ} - 2 x) + 36 0^{\circ} n

展开

18 0^{\circ} - (9 0^{\circ} - 2 x) + 36 0^{\circ} n : 18 0^{\circ} - 9 0^{\circ} + 2 x + 36 0^{\circ} n

18 0^{\circ} - (9 0^{\circ} - 2 x) + 36 0^{\circ} n

- (9 0^{\circ} - 2 x) : - 9 0^{\circ} + 2 x

- (9 0^{\circ} - 2 x)

打开括号

= - (9 0^{\circ}) - (- 2 x)

使用加减运算法则

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

= - 9 0^{\circ} + 2 x

= 18 0^{\circ} - 9 0^{\circ} + 2 x + 36 0^{\circ} n

7 0^{\circ} + x = 18 0^{\circ} - 9 0^{\circ} + 2 x + 36 0^{\circ} n

将

7 0^{\circ}

到右边

7 0^{\circ} + x = 18 0^{\circ} - 9 0^{\circ} + 2 x + 36 0^{\circ} n

两边减去

7 0^{\circ}

7 0^{\circ} + x - 7 0^{\circ} = 18 0^{\circ} - 9 0^{\circ} + 2 x + 36 0^{\circ} n - 7 0^{\circ}

化简

7 0^{\circ} + x - 7 0^{\circ} = 18 0^{\circ} - 9 0^{\circ} + 2 x + 36 0^{\circ} n - 7 0^{\circ}

化简

7 0^{\circ} + x - 7 0^{\circ} : x

7 0^{\circ} + x - 7 0^{\circ}

同类项相加:

7 0^{\circ} - 7 0^{\circ} = 0

= x

化简

18 0^{\circ} - 9 0^{\circ} + 2 x + 36 0^{\circ} n - 7 0^{\circ} : 2 x + 18 0^{\circ} + 36 0^{\circ} n - 16 0^{\circ}

18 0^{\circ} - 9 0^{\circ} + 2 x + 36 0^{\circ} n - 7 0^{\circ}

对同类项分组

= 2 x + 18 0^{\circ} + 36 0^{\circ} n - 9 0^{\circ} - 7 0^{\circ}

2, 18

的最小公倍数:

18

2, 18

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

18

质因数分解:

2 \cdot 3 \cdot 3

18

18

除以

218 = 9 \cdot 2

= 2 \cdot 9

9

除以

39 = 3 \cdot 3

= 2 \cdot 3 \cdot 3

2, 3

都是质数，因此无法进一步因数分解

= 2 \cdot 3 \cdot 3

将每个因子乘以它在

2

或

18

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}

= - 9 0^{\circ} - 7 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 - 126 0 ^{\circ}}{18}

同类项相加:

- 162 0^{\circ} - 126 0^{\circ} = - 288 0^{\circ}

= \frac{- 288 0 ^{\circ}}{18}

使用分式法则:

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

= - 16 0^{\circ}

约分:

2

= 2 x + 18 0^{\circ} + 36 0^{\circ} n - 16 0^{\circ}

x = 2 x + 18 0^{\circ} + 36 0^{\circ} n - 16 0^{\circ}

x = 2 x + 18 0^{\circ} + 36 0^{\circ} n - 16 0^{\circ}

x = 2 x + 18 0^{\circ} + 36 0^{\circ} n - 16 0^{\circ}

将

2 x

para o lado esquerdo

x = 2 x + 18 0^{\circ} + 36 0^{\circ} n - 16 0^{\circ}

两边减去

2 x

x - 2 x = 2 x + 18 0^{\circ} + 36 0^{\circ} n - 16 0^{\circ} - 2 x

化简

- x = 18 0^{\circ} + 36 0^{\circ} n - 16 0^{\circ}

- x = 18 0^{\circ} + 36 0^{\circ} n - 16 0^{\circ}

两边除以

- 1

- x = 18 0^{\circ} + 36 0^{\circ} n - 16 0^{\circ}

两边除以

- 1

\frac{- x}{- 1} = \frac{18 0 ^{\circ}}{- 1} + \frac{36 0 ^{\circ} n}{- 1} - \frac{16 0 ^{\circ}}{- 1}

化简

\frac{- x}{- 1} = \frac{18 0 ^{\circ}}{- 1} + \frac{36 0 ^{\circ} n}{- 1} - \frac{16 0 ^{\circ}}{- 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{18 0 ^{\circ}}{- 1} + \frac{36 0 ^{\circ} n}{- 1} - \frac{16 0 ^{\circ}}{- 1} : - \frac{18 0 ^{\circ} + 324 0 ^{\circ} n}{9}

\frac{18 0 ^{\circ}}{- 1} + \frac{36 0 ^{\circ} n}{- 1} - \frac{16 0 ^{\circ}}{- 1}

使用法则

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

= \frac{18 0 ^{\circ} + 36 0 ^{\circ} n - 16 0 ^{\circ}}{- 1}

使用分式法则:

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

= - \frac{18 0 ^{\circ} + 36 0 ^{\circ} n - 16 0 ^{\circ}}{1}

化简

18 0^{\circ} + 36 0^{\circ} n - 16 0^{\circ} : \frac{18 0 ^{\circ} + 324 0 ^{\circ} n}{9}

18 0^{\circ} + 36 0^{\circ} n - 16 0^{\circ}

将项转换为分式:

18 0^{\circ} = 18 0^{\circ}, 36 0^{\circ} n = \frac{36 0 ^{\circ} n 9}{9}

= 18 0^{\circ} + \frac{36 0 ^{\circ} n \cdot 9}{9} - 16 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 + 36 0 ^{\circ} n \cdot 9 - 144 0 ^{\circ}}{9}

18 0^{\circ} 9 + 36 0^{\circ} n \cdot 9 - 144 0^{\circ} = 18 0^{\circ} + 324 0^{\circ} n

18 0^{\circ} 9 + 36 0^{\circ} n \cdot 9 - 144 0^{\circ}

同类项相加:

162 0^{\circ} - 144 0^{\circ} = 18 0^{\circ}

= 18 0^{\circ} + 2 \cdot 162 0^{\circ} n

数字相乘:

2 \cdot 9 = 18

= 18 0^{\circ} + 324 0^{\circ} n

= \frac{18 0 ^{\circ} + 324 0 ^{\circ} n}{9}

= - \frac{\frac{18 0 ^{\circ} + 324 0 ^{\circ} n}{9}}{1}

使用分式法则:

\frac{a}{1} = a

= - \frac{18 0 ^{\circ} + 324 0 ^{\circ} n}{9}

x = - \frac{18 0 ^{\circ} + 324 0 ^{\circ} n}{9}

x = - \frac{18 0 ^{\circ} + 324 0 ^{\circ} n}{9}

x = - \frac{18 0 ^{\circ} + 324 0 ^{\circ} n}{9}

x = \frac{324 0 ^{\circ} n + 18 0 ^{\circ}}{27}, x = - \frac{18 0 ^{\circ} + 324 0 ^{\circ} n}{9}

x = \frac{324 0 ^{\circ} n + 18 0 ^{\circ}}{27}, x = - \frac{18 0 ^{\circ} + 324 0 ^{\circ} n}{9}

作图

流行的例子

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