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受欢迎的三角函数 >

sin(x-30)=cos(2x)

解答

sin (x - 3 0^{\circ}) = cos (2 x)

解答

x = \frac{108 0 ^{\circ} n + 36 0 ^{\circ}}{9}, x = - \frac{36 0 ^{\circ} + 108 0 ^{\circ} n}{3}

+1

弧度

x = \frac{2 π}{9} + \frac{6 π}{9} n, x = - \frac{2 π}{3} - \frac{6 π}{3} n

求解步骤

sin (x - 3 0^{\circ}) = cos (2 x)

使用三角恒等式改写

sin (x - 3 0^{\circ}) = cos (2 x)

利用以下特性:

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

sin (x - 3 0^{\circ}) = sin (9 0^{\circ} - 2 x)

sin (x - 3 0^{\circ}) = sin (9 0^{\circ} - 2 x)

使用反三角函数性质

sin (x - 3 0^{\circ}) = sin (9 0^{\circ} - 2 x)

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

x - 3 0^{\circ} = 9 0^{\circ} - 2 x + 36 0^{\circ} n, x - 3 0^{\circ} = 18 0^{\circ} - (9 0^{\circ} - 2 x) + 36 0^{\circ} n

x - 3 0^{\circ} = 9 0^{\circ} - 2 x + 36 0^{\circ} n, x - 3 0^{\circ} = 18 0^{\circ} - (9 0^{\circ} - 2 x) + 36 0^{\circ} n

x - 3 0^{\circ} = 9 0^{\circ} - 2 x + 36 0^{\circ} n : x = \frac{108 0 ^{\circ} n + 36 0 ^{\circ}}{9}

x - 3 0^{\circ} = 9 0^{\circ} - 2 x + 36 0^{\circ} n

将

3 0^{\circ}

到右边

x - 3 0^{\circ} = 9 0^{\circ} - 2 x + 36 0^{\circ} n

两边加上

3 0^{\circ}

x - 3 0^{\circ} + 3 0^{\circ} = 9 0^{\circ} - 2 x + 36 0^{\circ} n + 3 0^{\circ}

化简

x - 3 0^{\circ} + 3 0^{\circ} = 9 0^{\circ} - 2 x + 36 0^{\circ} n + 3 0^{\circ}

化简

x - 3 0^{\circ} + 3 0^{\circ} : x

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

同类项相加:

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

= x

化简

9 0^{\circ} - 2 x + 36 0^{\circ} n + 3 0^{\circ} : - 2 x + 36 0^{\circ} n + 12 0^{\circ}

9 0^{\circ} - 2 x + 36 0^{\circ} n + 3 0^{\circ}

对同类项分组

= - 2 x + 36 0^{\circ} n + 9 0^{\circ} + 3 0^{\circ}

2, 6

的最小公倍数:

6

2, 6

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

6

质因数分解:

2 \cdot 3

6

6

除以

26 = 3 \cdot 2

= 2 \cdot 3

2, 3

都是质数，因此无法进一步因数分解

= 2 \cdot 3

将每个因子乘以它在

2

或

6

中出现的最多次数

= 2 \cdot 3

数字相乘:

2 \cdot 3 = 6

= 6

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

6

对于

9 0^{\circ} :

将分母和分子乘以

3

9 0^{\circ} = \frac{18 0 ^{\circ} 3}{2 \cdot 3} = 9 0^{\circ}

= 9 0^{\circ} + 3 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} 3 + 18 0 ^{\circ}}{6}

同类项相加:

54 0^{\circ} + 18 0^{\circ} = 72 0^{\circ}

= 12 0^{\circ}

约分:

2

= - 2 x + 36 0^{\circ} n + 12 0^{\circ}

x = - 2 x + 36 0^{\circ} n + 12 0^{\circ}

x = - 2 x + 36 0^{\circ} n + 12 0^{\circ}

x = - 2 x + 36 0^{\circ} n + 12 0^{\circ}

将

2 x

para o lado esquerdo

x = - 2 x + 36 0^{\circ} n + 12 0^{\circ}

两边加上

2 x

x + 2 x = - 2 x + 36 0^{\circ} n + 12 0^{\circ} + 2 x

化简

3 x = 36 0^{\circ} n + 12 0^{\circ}

3 x = 36 0^{\circ} n + 12 0^{\circ}

两边除以

3

3 x = 36 0^{\circ} n + 12 0^{\circ}

两边除以

3

\frac{3 x}{3} = \frac{36 0 ^{\circ} n}{3} + \frac{12 0 ^{\circ}}{3}

化简

\frac{3 x}{3} = \frac{36 0 ^{\circ} n}{3} + \frac{12 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{12 0 ^{\circ}}{3} : \frac{108 0 ^{\circ} n + 36 0 ^{\circ}}{9}

\frac{36 0 ^{\circ} n}{3} + \frac{12 0 ^{\circ}}{3}

使用法则

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

= \frac{36 0 ^{\circ} n + 12 0 ^{\circ}}{3}

化简

36 0^{\circ} n + 12 0^{\circ} : \frac{108 0 ^{\circ} n + 36 0 ^{\circ}}{3}

36 0^{\circ} n + 12 0^{\circ}

将项转换为分式:

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

= \frac{36 0 ^{\circ} n \cdot 3}{3} + 12 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 3 + 36 0 ^{\circ}}{3}

数字相乘:

2 \cdot 3 = 6

= \frac{108 0 ^{\circ} n + 36 0 ^{\circ}}{3}

= \frac{\frac{108 0 ^{\circ} n + 36 0 ^{\circ}}{3}}{3}

使用分式法则:

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

= \frac{108 0 ^{\circ} n + 36 0 ^{\circ}}{3 \cdot 3}

数字相乘:

3 \cdot 3 = 9

= \frac{108 0 ^{\circ} n + 36 0 ^{\circ}}{9}

x = \frac{108 0 ^{\circ} n + 36 0 ^{\circ}}{9}

x = \frac{108 0 ^{\circ} n + 36 0 ^{\circ}}{9}

x = \frac{108 0 ^{\circ} n + 36 0 ^{\circ}}{9}

x - 3 0^{\circ} = 18 0^{\circ} - (9 0^{\circ} - 2 x) + 36 0^{\circ} n : x = - \frac{36 0 ^{\circ} + 108 0 ^{\circ} n}{3}

x - 3 0^{\circ} = 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

x - 3 0^{\circ} = 18 0^{\circ} - 9 0^{\circ} + 2 x + 36 0^{\circ} n

将

3 0^{\circ}

到右边

x - 3 0^{\circ} = 18 0^{\circ} - 9 0^{\circ} + 2 x + 36 0^{\circ} n

两边加上

3 0^{\circ}

x - 3 0^{\circ} + 3 0^{\circ} = 18 0^{\circ} - 9 0^{\circ} + 2 x + 36 0^{\circ} n + 3 0^{\circ}

化简

x - 3 0^{\circ} + 3 0^{\circ} = 18 0^{\circ} - 9 0^{\circ} + 2 x + 36 0^{\circ} n + 3 0^{\circ}

化简

x - 3 0^{\circ} + 3 0^{\circ} : x

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

同类项相加:

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

= x

化简

18 0^{\circ} - 9 0^{\circ} + 2 x + 36 0^{\circ} n + 3 0^{\circ} : 2 x + 18 0^{\circ} + 36 0^{\circ} n - 6 0^{\circ}

18 0^{\circ} - 9 0^{\circ} + 2 x + 36 0^{\circ} n + 3 0^{\circ}

对同类项分组

= 2 x + 18 0^{\circ} + 36 0^{\circ} n - 9 0^{\circ} + 3 0^{\circ}

2, 6

的最小公倍数:

6

2, 6

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

6

质因数分解:

2 \cdot 3

6

6

除以

26 = 3 \cdot 2

= 2 \cdot 3

2, 3

都是质数，因此无法进一步因数分解

= 2 \cdot 3

将每个因子乘以它在

2

或

6

中出现的最多次数

= 2 \cdot 3

数字相乘:

2 \cdot 3 = 6

= 6

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

6

对于

9 0^{\circ} :

将分母和分子乘以

3

9 0^{\circ} = \frac{18 0 ^{\circ} 3}{2 \cdot 3} = 9 0^{\circ}

= - 9 0^{\circ} + 3 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} 3 + 18 0 ^{\circ}}{6}

同类项相加:

- 54 0^{\circ} + 18 0^{\circ} = - 36 0^{\circ}

= \frac{- 36 0 ^{\circ}}{6}

使用分式法则:

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

= - 6 0^{\circ}

约分:

2

= 2 x + 18 0^{\circ} + 36 0^{\circ} n - 6 0^{\circ}

x = 2 x + 18 0^{\circ} + 36 0^{\circ} n - 6 0^{\circ}

x = 2 x + 18 0^{\circ} + 36 0^{\circ} n - 6 0^{\circ}

x = 2 x + 18 0^{\circ} + 36 0^{\circ} n - 6 0^{\circ}

将

2 x

para o lado esquerdo

x = 2 x + 18 0^{\circ} + 36 0^{\circ} n - 6 0^{\circ}

两边减去

2 x

x - 2 x = 2 x + 18 0^{\circ} + 36 0^{\circ} n - 6 0^{\circ} - 2 x

化简

- x = 18 0^{\circ} + 36 0^{\circ} n - 6 0^{\circ}

- x = 18 0^{\circ} + 36 0^{\circ} n - 6 0^{\circ}

两边除以

- 1

- x = 18 0^{\circ} + 36 0^{\circ} n - 6 0^{\circ}

两边除以

- 1

\frac{- x}{- 1} = \frac{18 0 ^{\circ}}{- 1} + \frac{36 0 ^{\circ} n}{- 1} - \frac{6 0 ^{\circ}}{- 1}

化简

\frac{- x}{- 1} = \frac{18 0 ^{\circ}}{- 1} + \frac{36 0 ^{\circ} n}{- 1} - \frac{6 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{6 0 ^{\circ}}{- 1} : - \frac{36 0 ^{\circ} + 108 0 ^{\circ} n}{3}

\frac{18 0 ^{\circ}}{- 1} + \frac{36 0 ^{\circ} n}{- 1} - \frac{6 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 - 6 0 ^{\circ}}{- 1}

使用分式法则:

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

= - \frac{18 0 ^{\circ} + 36 0 ^{\circ} n - 6 0 ^{\circ}}{1}

化简

18 0^{\circ} + 36 0^{\circ} n - 6 0^{\circ} : \frac{36 0 ^{\circ} + 108 0 ^{\circ} n}{3}

18 0^{\circ} + 36 0^{\circ} n - 6 0^{\circ}

将项转换为分式:

18 0^{\circ} = 18 0^{\circ}, 36 0^{\circ} n = \frac{36 0 ^{\circ} n 3}{3}

= 18 0^{\circ} + \frac{36 0 ^{\circ} n \cdot 3}{3} - 6 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} 3 + 36 0 ^{\circ} n \cdot 3 - 18 0 ^{\circ}}{3}

18 0^{\circ} 3 + 36 0^{\circ} n \cdot 3 - 18 0^{\circ} = 36 0^{\circ} + 108 0^{\circ} n

18 0^{\circ} 3 + 36 0^{\circ} n \cdot 3 - 18 0^{\circ}

同类项相加:

54 0^{\circ} - 18 0^{\circ} = 36 0^{\circ}

= 36 0^{\circ} + 2 \cdot 54 0^{\circ} n

数字相乘:

2 \cdot 3 = 6

= 36 0^{\circ} + 108 0^{\circ} n

= \frac{36 0 ^{\circ} + 108 0 ^{\circ} n}{3}

= - \frac{\frac{36 0 ^{\circ} + 108 0 ^{\circ} n}{3}}{1}

使用分式法则:

\frac{a}{1} = a

= - \frac{36 0 ^{\circ} + 108 0 ^{\circ} n}{3}

x = - \frac{36 0 ^{\circ} + 108 0 ^{\circ} n}{3}

x = - \frac{36 0 ^{\circ} + 108 0 ^{\circ} n}{3}

x = - \frac{36 0 ^{\circ} + 108 0 ^{\circ} n}{3}

x = \frac{108 0 ^{\circ} n + 36 0 ^{\circ}}{9}, x = - \frac{36 0 ^{\circ} + 108 0 ^{\circ} n}{3}

x = \frac{108 0 ^{\circ} n + 36 0 ^{\circ}}{9}, x = - \frac{36 0 ^{\circ} + 108 0 ^{\circ} n}{3}

作图

流行的例子

sin (x) = sec (x)

sin(x-pi/3)=0.4

sin (x - \frac{π}{3}) = 0.4

2cos^2(a)=cos(a)

2 cos^{2} (a) = cos (a)

\frac{1}{2} = cos (2 θ)

(tan(x)-1)(2sin(x)+1)=0

(tan (x) - 1) (2 sin (x) + 1) = 0