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受欢迎的三角函数 >

cos(3x+20)=-sin(x-60)

解答

cos (3 x + 20) = - sin (x - 6 0^{\circ})

解答

x = \frac{216 0 ^{\circ} n + 18 0 ^{\circ} - 120}{12}, x = - \frac{18 0 ^{\circ} + 216 0 ^{\circ} n + 120}{24}

+1

弧度

x = \frac{π}{12} - 10 + \frac{12 π}{12} n, x = - 5 - \frac{π}{24} - \frac{12 π}{24} n

求解步骤

cos (3 x + 20) = - sin (x - 6 0^{\circ})

使用三角恒等式改写

cos (3 x + 20) = - sin (x - 6 0^{\circ})

利用以下特性:

- sin (x) = sin (- x)

cos (3 x + 20) = sin (- (x - 6 0^{\circ}))

利用以下特性:

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

cos (3 x + 20) = sin (9 0^{\circ} - (3 x + 20))

cos (3 x + 20) = sin (9 0^{\circ} - (3 x + 20))

使用反三角函数性质

cos (3 x + 20) = sin (9 0^{\circ} - (3 x + 20))

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

- (x - 6 0^{\circ}) = 9 0^{\circ} - (3 x + 20) + 36 0^{\circ} n, - (x - 6 0^{\circ}) = 18 0^{\circ} - (9 0^{\circ} - (3 x + 20)) + 36 0^{\circ} n

- (x - 6 0^{\circ}) = 9 0^{\circ} - (3 x + 20) + 36 0^{\circ} n, - (x - 6 0^{\circ}) = 18 0^{\circ} - (9 0^{\circ} - (3 x + 20)) + 36 0^{\circ} n

- (x - 6 0^{\circ}) = 9 0^{\circ} - (3 x + 20) + 36 0^{\circ} n : x = \frac{216 0 ^{\circ} n + 18 0 ^{\circ} - 120}{12}

- (x - 6 0^{\circ}) = 9 0^{\circ} - (3 x + 20) + 36 0^{\circ} n

展开

- (x - 6 0^{\circ}) : - x + 6 0^{\circ}

- (x - 6 0^{\circ})

打开括号

= - (x) - (- 6 0^{\circ})

使用加减运算法则

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

= - x + 6 0^{\circ}

展开

9 0^{\circ} - (3 x + 20) + 36 0^{\circ} n : 9 0^{\circ} - 3 x - 20 + 36 0^{\circ} n

9 0^{\circ} - (3 x + 20) + 36 0^{\circ} n

- (3 x + 20) : - 3 x - 20

- (3 x + 20)

打开括号

= - (3 x) - (20)

使用加减运算法则

+ (- a) = - a

= - 3 x - 20

= 9 0^{\circ} - 3 x - 20 + 36 0^{\circ} n

- x + 6 0^{\circ} = 9 0^{\circ} - 3 x - 20 + 36 0^{\circ} n

将

6 0^{\circ}

到右边

- x + 6 0^{\circ} = 9 0^{\circ} - 3 x - 20 + 36 0^{\circ} n

两边减去

6 0^{\circ}

- x + 6 0^{\circ} - 6 0^{\circ} = 9 0^{\circ} - 3 x - 20 + 36 0^{\circ} n - 6 0^{\circ}

化简

- x + 6 0^{\circ} - 6 0^{\circ} = 9 0^{\circ} - 3 x - 20 + 36 0^{\circ} n - 6 0^{\circ}

化简

- x + 6 0^{\circ} - 6 0^{\circ} : - x

- x + 6 0^{\circ} - 6 0^{\circ}

同类项相加:

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

= - x

化简

9 0^{\circ} - 3 x - 20 + 36 0^{\circ} n - 6 0^{\circ} : - 3 x + 36 0^{\circ} n + 3 0^{\circ} - 20

9 0^{\circ} - 3 x - 20 + 36 0^{\circ} n - 6 0^{\circ}

对同类项分组

= - 3 x + 36 0^{\circ} n + 9 0^{\circ} - 6 0^{\circ} - 20

合并分式

9 0^{\circ} - 6 0^{\circ} : 3 0^{\circ}

9 0^{\circ} - 6 0^{\circ}

2, 3

的最小公倍数:

6

2, 3

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

3

质因数分解:

3

3

3

是质数，因此无法因数分解

= 3

将每个因子乘以它在

2

或

3

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}

对于

6 0^{\circ} :

将分母和分子乘以

2

6 0^{\circ} = \frac{18 0 ^{\circ} 2}{3 \cdot 2} = 6 0^{\circ}

= 9 0^{\circ} - 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 - 18 0 ^{\circ} 2}{6}

同类项相加:

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

= 3 0^{\circ}

= - 3 x + 36 0^{\circ} n + 3 0^{\circ} - 20

- x = - 3 x + 36 0^{\circ} n + 3 0^{\circ} - 20

- x = - 3 x + 36 0^{\circ} n + 3 0^{\circ} - 20

- x = - 3 x + 36 0^{\circ} n + 3 0^{\circ} - 20

将

3 x

para o lado esquerdo

- x = - 3 x + 36 0^{\circ} n + 3 0^{\circ} - 20

两边加上

3 x

- x + 3 x = - 3 x + 36 0^{\circ} n + 3 0^{\circ} - 20 + 3 x

化简

2 x = 36 0^{\circ} n + 3 0^{\circ} - 20

2 x = 36 0^{\circ} n + 3 0^{\circ} - 20

两边除以

2

2 x = 36 0^{\circ} n + 3 0^{\circ} - 20

两边除以

2

\frac{2 x}{2} = \frac{36 0 ^{\circ} n}{2} + \frac{3 0 ^{\circ}}{2} - \frac{20}{2}

化简

\frac{2 x}{2} = \frac{36 0 ^{\circ} n}{2} + \frac{3 0 ^{\circ}}{2} - \frac{20}{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{3 0 ^{\circ}}{2} - \frac{20}{2} : \frac{216 0 ^{\circ} n + 18 0 ^{\circ} - 120}{12}

\frac{36 0 ^{\circ} n}{2} + \frac{3 0 ^{\circ}}{2} - \frac{20}{2}

使用法则

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

= \frac{36 0 ^{\circ} n + 3 0 ^{\circ} - 20}{2}

化简

36 0^{\circ} n + 3 0^{\circ} - 20 : \frac{216 0 ^{\circ} n + 18 0 ^{\circ} - 120}{6}

36 0^{\circ} n + 3 0^{\circ} - 20

将项转换为分式:

36 0^{\circ} n = \frac{36 0 ^{\circ} n 6}{6}, 20 = \frac{20 \cdot 6}{6}

= \frac{36 0 ^{\circ} n \cdot 6}{6} + 3 0^{\circ} - \frac{20 \cdot 6}{6}

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 6 + 18 0 ^{\circ} - 20 \cdot 6}{6}

36 0^{\circ} n \cdot 6 + 18 0^{\circ} - 20 \cdot 6 = 216 0^{\circ} n + 18 0^{\circ} - 120

36 0^{\circ} n \cdot 6 + 18 0^{\circ} - 20 \cdot 6

数字相乘:

2 \cdot 6 = 12

= 216 0^{\circ} n + 18 0^{\circ} - 20 \cdot 6

数字相乘:

20 \cdot 6 = 120

= 216 0^{\circ} n + 18 0^{\circ} - 120

= \frac{216 0 ^{\circ} n + 18 0 ^{\circ} - 120}{6}

= \frac{\frac{216 0 ^{\circ} n + 18 0 ^{\circ} - 120}{6}}{2}

使用分式法则:

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

= \frac{216 0 ^{\circ} n + 18 0 ^{\circ} - 120}{6 \cdot 2}

数字相乘:

6 \cdot 2 = 12

= \frac{216 0 ^{\circ} n + 18 0 ^{\circ} - 120}{12}

x = \frac{216 0 ^{\circ} n + 18 0 ^{\circ} - 120}{12}

x = \frac{216 0 ^{\circ} n + 18 0 ^{\circ} - 120}{12}

x = \frac{216 0 ^{\circ} n + 18 0 ^{\circ} - 120}{12}

- (x - 6 0^{\circ}) = 18 0^{\circ} - (9 0^{\circ} - (3 x + 20)) + 36 0^{\circ} n : x = - \frac{18 0 ^{\circ} + 216 0 ^{\circ} n + 120}{24}

- (x - 6 0^{\circ}) = 18 0^{\circ} - (9 0^{\circ} - (3 x + 20)) + 36 0^{\circ} n

展开

- (x - 6 0^{\circ}) : - x + 6 0^{\circ}

- (x - 6 0^{\circ})

打开括号

= - (x) - (- 6 0^{\circ})

使用加减运算法则

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

= - x + 6 0^{\circ}

展开

18 0^{\circ} - (9 0^{\circ} - (3 x + 20)) + 36 0^{\circ} n : 18 0^{\circ} - 9 0^{\circ} + 3 x + 20 + 36 0^{\circ} n

18 0^{\circ} - (9 0^{\circ} - (3 x + 20)) + 36 0^{\circ} n

- (3 x + 20) : - 3 x - 20

- (3 x + 20)

打开括号

= - (3 x) - (20)

使用加减运算法则

+ (- a) = - a

= - 3 x - 20

= 18 0^{\circ} - (- 3 x + 9 0^{\circ} - 20) + 36 0^{\circ} n

- (9 0^{\circ} - 3 x - 20) : - 9 0^{\circ} + 3 x + 20

- (9 0^{\circ} - 3 x - 20)

打开括号

= - (9 0^{\circ}) - (- 3 x) - (- 20)

使用加减运算法则

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

= - 9 0^{\circ} + 3 x + 20

= 18 0^{\circ} - 9 0^{\circ} + 3 x + 20 + 36 0^{\circ} n

- x + 6 0^{\circ} = 18 0^{\circ} - 9 0^{\circ} + 3 x + 20 + 36 0^{\circ} n

将

6 0^{\circ}

到右边

- x + 6 0^{\circ} = 18 0^{\circ} - 9 0^{\circ} + 3 x + 20 + 36 0^{\circ} n

两边减去

6 0^{\circ}

- x + 6 0^{\circ} - 6 0^{\circ} = 18 0^{\circ} - 9 0^{\circ} + 3 x + 20 + 36 0^{\circ} n - 6 0^{\circ}

化简

- x + 6 0^{\circ} - 6 0^{\circ} = 18 0^{\circ} - 9 0^{\circ} + 3 x + 20 + 36 0^{\circ} n - 6 0^{\circ}

化简

- x + 6 0^{\circ} - 6 0^{\circ} : - x

- x + 6 0^{\circ} - 6 0^{\circ}

同类项相加:

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

= - x

化简

18 0^{\circ} - 9 0^{\circ} + 3 x + 20 + 36 0^{\circ} n - 6 0^{\circ} : 3 x + 18 0^{\circ} + 36 0^{\circ} n - 15 0^{\circ} + 20

18 0^{\circ} - 9 0^{\circ} + 3 x + 20 + 36 0^{\circ} n - 6 0^{\circ}

对同类项分组

= 3 x + 18 0^{\circ} + 36 0^{\circ} n - 9 0^{\circ} - 6 0^{\circ} + 20

合并分式

- 9 0^{\circ} - 6 0^{\circ} : - 15 0^{\circ}

- 9 0^{\circ} - 6 0^{\circ}

2, 3

的最小公倍数:

6

2, 3

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

3

质因数分解:

3

3

3

是质数，因此无法因数分解

= 3

将每个因子乘以它在

2

或

3

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}

对于

6 0^{\circ} :

将分母和分子乘以

2

6 0^{\circ} = \frac{18 0 ^{\circ} 2}{3 \cdot 2} = 6 0^{\circ}

= - 9 0^{\circ} - 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 - 18 0 ^{\circ} 2}{6}

同类项相加:

- 54 0^{\circ} - 36 0^{\circ} = - 90 0^{\circ}

= \frac{- 90 0 ^{\circ}}{6}

使用分式法则:

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

= - 15 0^{\circ}

= 3 x + 18 0^{\circ} + 36 0^{\circ} n - 15 0^{\circ} + 20

- x = 3 x + 18 0^{\circ} + 36 0^{\circ} n - 15 0^{\circ} + 20

- x = 3 x + 18 0^{\circ} + 36 0^{\circ} n - 15 0^{\circ} + 20

- x = 3 x + 18 0^{\circ} + 36 0^{\circ} n - 15 0^{\circ} + 20

将

3 x

para o lado esquerdo

- x = 3 x + 18 0^{\circ} + 36 0^{\circ} n - 15 0^{\circ} + 20

两边减去

3 x

- x - 3 x = 3 x + 18 0^{\circ} + 36 0^{\circ} n - 15 0^{\circ} + 20 - 3 x

化简

- 4 x = 18 0^{\circ} + 36 0^{\circ} n - 15 0^{\circ} + 20

- 4 x = 18 0^{\circ} + 36 0^{\circ} n - 15 0^{\circ} + 20

两边除以

- 4

- 4 x = 18 0^{\circ} + 36 0^{\circ} n - 15 0^{\circ} + 20

两边除以

- 4

\frac{- 4 x}{- 4} = \frac{18 0 ^{\circ}}{- 4} + \frac{36 0 ^{\circ} n}{- 4} - \frac{15 0 ^{\circ}}{- 4} + \frac{20}{- 4}

化简

\frac{- 4 x}{- 4} = \frac{18 0 ^{\circ}}{- 4} + \frac{36 0 ^{\circ} n}{- 4} - \frac{15 0 ^{\circ}}{- 4} + \frac{20}{- 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{15 0 ^{\circ}}{- 4} + \frac{20}{- 4} : - \frac{18 0 ^{\circ} + 216 0 ^{\circ} n + 120}{24}

\frac{18 0 ^{\circ}}{- 4} + \frac{36 0 ^{\circ} n}{- 4} - \frac{15 0 ^{\circ}}{- 4} + \frac{20}{- 4}

对同类项分组

= \frac{18 0 ^{\circ}}{- 4} + \frac{20}{- 4} + \frac{36 0 ^{\circ} n}{- 4} - \frac{15 0 ^{\circ}}{- 4}

使用法则

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

= \frac{18 0 ^{\circ} + 20 + 36 0 ^{\circ} n - 15 0 ^{\circ}}{- 4}

使用分式法则:

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

= - \frac{18 0 ^{\circ} + 20 + 36 0 ^{\circ} n - 15 0 ^{\circ}}{4}

化简

18 0^{\circ} + 20 + 36 0^{\circ} n - 15 0^{\circ} : \frac{18 0 ^{\circ} + 216 0 ^{\circ} n + 120}{6}

18 0^{\circ} + 20 + 36 0^{\circ} n - 15 0^{\circ}

将项转换为分式:

18 0^{\circ} = 18 0^{\circ}, 20 = \frac{20 \cdot 6}{6}, 36 0^{\circ} n = \frac{36 0 ^{\circ} n 6}{6}

= 18 0^{\circ} + \frac{20 \cdot 6}{6} + \frac{36 0 ^{\circ} n \cdot 6}{6} - 15 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} 6 + 20 \cdot 6 + 36 0 ^{\circ} n \cdot 6 - 90 0 ^{\circ}}{6}

18 0^{\circ} 6 + 20 \cdot 6 + 36 0^{\circ} n \cdot 6 - 90 0^{\circ} = 18 0^{\circ} + 216 0^{\circ} n + 120

18 0^{\circ} 6 + 20 \cdot 6 + 36 0^{\circ} n \cdot 6 - 90 0^{\circ}

对同类项分组

= 108 0^{\circ} - 90 0^{\circ} + 2 \cdot 108 0^{\circ} n + 20 \cdot 6

同类项相加:

108 0^{\circ} - 90 0^{\circ} = 18 0^{\circ}

= 18 0^{\circ} + 2 \cdot 108 0^{\circ} n + 20 \cdot 6

数字相乘:

2 \cdot 6 = 12

= 18 0^{\circ} + 216 0^{\circ} n + 20 \cdot 6

数字相乘:

20 \cdot 6 = 120

= 18 0^{\circ} + 216 0^{\circ} n + 120

= \frac{18 0 ^{\circ} + 216 0 ^{\circ} n + 120}{6}

= - \frac{\frac{18 0 ^{\circ} + 216 0 ^{\circ} n + 120}{6}}{4}

化简

\frac{\frac{18 0 ^{\circ} + 216 0 ^{\circ} n + 120}{6}}{4} : \frac{18 0 ^{\circ} + 216 0 ^{\circ} n + 120}{24}

\frac{\frac{18 0 ^{\circ} + 216 0 ^{\circ} n + 120}{6}}{4}

使用分式法则:

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

= \frac{18 0 ^{\circ} + 216 0 ^{\circ} n + 120}{6 \cdot 4}

数字相乘:

6 \cdot 4 = 24

= \frac{18 0 ^{\circ} + 216 0 ^{\circ} n + 120}{24}

= - \frac{18 0 ^{\circ} + 216 0 ^{\circ} n + 120}{24}

x = - \frac{18 0 ^{\circ} + 216 0 ^{\circ} n + 120}{24}

x = - \frac{18 0 ^{\circ} + 216 0 ^{\circ} n + 120}{24}

x = - \frac{18 0 ^{\circ} + 216 0 ^{\circ} n + 120}{24}

x = \frac{216 0 ^{\circ} n + 18 0 ^{\circ} - 120}{12}, x = - \frac{18 0 ^{\circ} + 216 0 ^{\circ} n + 120}{24}

x = \frac{216 0 ^{\circ} n + 18 0 ^{\circ} - 120}{12}, x = - \frac{18 0 ^{\circ} + 216 0 ^{\circ} n + 120}{24}

作图

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