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受欢迎的三角函数 >

sin(2x-10)=cos(x+10)

解答

sin (2 x - 10) = cos (x + 1 0^{\circ})

解答

x = \frac{324 0 ^{\circ} n + 72 0 ^{\circ} + 90}{27}, x = 18 0^{\circ} - 8 0^{\circ} + 36 0^{\circ} n + 10

+1

弧度

x = \frac{4 π}{27} + \frac{10}{3} + \frac{18 π}{27} n, x = π - \frac{4 π}{9} + 10 + 2 πn

求解步骤

sin (2 x - 10) = cos (x + 1 0^{\circ})

使用三角恒等式改写

sin (2 x - 10) = cos (x + 1 0^{\circ})

利用以下特性:

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

sin (2 x - 10) = sin (9 0^{\circ} - (x + 1 0^{\circ}))

sin (2 x - 10) = sin (9 0^{\circ} - (x + 1 0^{\circ}))

使用反三角函数性质

sin (2 x - 10) = sin (9 0^{\circ} - (x + 1 0^{\circ}))

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

2 x - 10 = 9 0^{\circ} - (x + 1 0^{\circ}) + 36 0^{\circ} n, 2 x - 10 = 18 0^{\circ} - (9 0^{\circ} - (x + 1 0^{\circ})) + 36 0^{\circ} n

2 x - 10 = 9 0^{\circ} - (x + 1 0^{\circ}) + 36 0^{\circ} n, 2 x - 10 = 18 0^{\circ} - (9 0^{\circ} - (x + 1 0^{\circ})) + 36 0^{\circ} n

2 x - 10 = 9 0^{\circ} - (x + 1 0^{\circ}) + 36 0^{\circ} n : x = \frac{324 0 ^{\circ} n + 72 0 ^{\circ} + 90}{27}

2 x - 10 = 9 0^{\circ} - (x + 1 0^{\circ}) + 36 0^{\circ} n

展开

9 0^{\circ} - (x + 1 0^{\circ}) + 36 0^{\circ} n : - x + 36 0^{\circ} n + 8 0^{\circ}

9 0^{\circ} - (x + 1 0^{\circ}) + 36 0^{\circ} n

- (x + 1 0^{\circ}) : - x - 1 0^{\circ}

- (x + 1 0^{\circ})

打开括号

= - (x) - (1 0^{\circ})

使用加减运算法则

+ (- a) = - a

= - x - 1 0^{\circ}

= 9 0^{\circ} - x - 1 0^{\circ} + 36 0^{\circ} n

化简

9 0^{\circ} - x - 1 0^{\circ} + 36 0^{\circ} n : - x + 36 0^{\circ} n + 8 0^{\circ}

9 0^{\circ} - x - 1 0^{\circ} + 36 0^{\circ} n

对同类项分组

= - x + 36 0^{\circ} n + 9 0^{\circ} - 1 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} - 1 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 - 18 0 ^{\circ}}{18}

同类项相加:

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

= 8 0^{\circ}

约分:

2

= - x + 36 0^{\circ} n + 8 0^{\circ}

= - x + 36 0^{\circ} n + 8 0^{\circ}

2 x - 10 = - x + 36 0^{\circ} n + 8 0^{\circ}

将

10

到右边

2 x - 10 = - x + 36 0^{\circ} n + 8 0^{\circ}

两边加上

10

2 x - 10 + 10 = - x + 36 0^{\circ} n + 8 0^{\circ} + 10

化简

2 x = - x + 36 0^{\circ} n + 8 0^{\circ} + 10

2 x = - x + 36 0^{\circ} n + 8 0^{\circ} + 10

将

x

para o lado esquerdo

2 x = - x + 36 0^{\circ} n + 8 0^{\circ} + 10

两边加上

x

2 x + x = - x + 36 0^{\circ} n + 8 0^{\circ} + 10 + x

化简

3 x = 36 0^{\circ} n + 8 0^{\circ} + 10

3 x = 36 0^{\circ} n + 8 0^{\circ} + 10

两边除以

3

3 x = 36 0^{\circ} n + 8 0^{\circ} + 10

两边除以

3

\frac{3 x}{3} = \frac{36 0 ^{\circ} n}{3} + \frac{8 0 ^{\circ}}{3} + \frac{10}{3}

化简

\frac{3 x}{3} = \frac{36 0 ^{\circ} n}{3} + \frac{8 0 ^{\circ}}{3} + \frac{10}{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{8 0 ^{\circ}}{3} + \frac{10}{3} : \frac{324 0 ^{\circ} n + 72 0 ^{\circ} + 90}{27}

\frac{36 0 ^{\circ} n}{3} + \frac{8 0 ^{\circ}}{3} + \frac{10}{3}

使用法则

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

= \frac{36 0 ^{\circ} n + 8 0 ^{\circ} + 10}{3}

化简

36 0^{\circ} n + 8 0^{\circ} + 10 : \frac{324 0 ^{\circ} n + 72 0 ^{\circ} + 90}{9}

36 0^{\circ} n + 8 0^{\circ} + 10

将项转换为分式:

36 0^{\circ} n = \frac{36 0 ^{\circ} n 9}{9}, 10 = \frac{10 \cdot 9}{9}

= \frac{36 0 ^{\circ} n \cdot 9}{9} + 8 0^{\circ} + \frac{10 \cdot 9}{9}

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 + 72 0 ^{\circ} + 10 \cdot 9}{9}

36 0^{\circ} n \cdot 9 + 72 0^{\circ} + 10 \cdot 9 = 324 0^{\circ} n + 72 0^{\circ} + 90

36 0^{\circ} n \cdot 9 + 72 0^{\circ} + 10 \cdot 9

数字相乘:

2 \cdot 9 = 18

= 324 0^{\circ} n + 72 0^{\circ} + 10 \cdot 9

数字相乘:

10 \cdot 9 = 90

= 324 0^{\circ} n + 72 0^{\circ} + 90

= \frac{324 0 ^{\circ} n + 72 0 ^{\circ} + 90}{9}

= \frac{\frac{324 0 ^{\circ} n + 72 0 ^{\circ} + 90}{9}}{3}

使用分式法则:

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

= \frac{324 0 ^{\circ} n + 72 0 ^{\circ} + 90}{9 \cdot 3}

数字相乘:

9 \cdot 3 = 27

= \frac{324 0 ^{\circ} n + 72 0 ^{\circ} + 90}{27}

x = \frac{324 0 ^{\circ} n + 72 0 ^{\circ} + 90}{27}

x = \frac{324 0 ^{\circ} n + 72 0 ^{\circ} + 90}{27}

x = \frac{324 0 ^{\circ} n + 72 0 ^{\circ} + 90}{27}

2 x - 10 = 18 0^{\circ} - (9 0^{\circ} - (x + 1 0^{\circ})) + 36 0^{\circ} n : x = 18 0^{\circ} - 8 0^{\circ} + 36 0^{\circ} n + 10

2 x - 10 = 18 0^{\circ} - (9 0^{\circ} - (x + 1 0^{\circ})) + 36 0^{\circ} n

展开

18 0^{\circ} - (9 0^{\circ} - (x + 1 0^{\circ})) + 36 0^{\circ} n : 18 0^{\circ} + x - 8 0^{\circ} + 36 0^{\circ} n

18 0^{\circ} - (9 0^{\circ} - (x + 1 0^{\circ})) + 36 0^{\circ} n

乘开

9 0^{\circ} - (x + 1 0^{\circ}) : - x + 8 0^{\circ}

9 0^{\circ} - (x + 1 0^{\circ})

- (x + 1 0^{\circ}) : - x - 1 0^{\circ}

- (x + 1 0^{\circ})

打开括号

= - (x) - (1 0^{\circ})

使用加减运算法则

+ (- a) = - a

= - x - 1 0^{\circ}

= 9 0^{\circ} - x - 1 0^{\circ}

化简

9 0^{\circ} - x - 1 0^{\circ} : - x + 8 0^{\circ}

9 0^{\circ} - x - 1 0^{\circ}

对同类项分组

= - x + 9 0^{\circ} - 1 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} - 1 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 - 18 0 ^{\circ}}{18}

同类项相加:

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

= 8 0^{\circ}

约分:

2

= - x + 8 0^{\circ}

= - x + 8 0^{\circ}

= 18 0^{\circ} - (- x + 8 0^{\circ}) + 36 0^{\circ} n

- (- x + 8 0^{\circ}) : x - 8 0^{\circ}

- (- x + 8 0^{\circ})

打开括号

= - (- x) - (8 0^{\circ})

使用加减运算法则

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

= x - 8 0^{\circ}

= 18 0^{\circ} + x - 8 0^{\circ} + 36 0^{\circ} n

2 x - 10 = 18 0^{\circ} + x - 8 0^{\circ} + 36 0^{\circ} n

将

10

到右边

2 x - 10 = 18 0^{\circ} + x - 8 0^{\circ} + 36 0^{\circ} n

两边加上

10

2 x - 10 + 10 = 18 0^{\circ} + x - 8 0^{\circ} + 36 0^{\circ} n + 10

化简

2 x = 18 0^{\circ} + x - 8 0^{\circ} + 36 0^{\circ} n + 10

2 x = 18 0^{\circ} + x - 8 0^{\circ} + 36 0^{\circ} n + 10

将

x

para o lado esquerdo

2 x = 18 0^{\circ} + x - 8 0^{\circ} + 36 0^{\circ} n + 10

两边减去

x

2 x - x = 18 0^{\circ} + x - 8 0^{\circ} + 36 0^{\circ} n + 10 - x

化简

x = 18 0^{\circ} - 8 0^{\circ} + 36 0^{\circ} n + 10

x = 18 0^{\circ} - 8 0^{\circ} + 36 0^{\circ} n + 10

x = \frac{324 0 ^{\circ} n + 72 0 ^{\circ} + 90}{27}, x = 18 0^{\circ} - 8 0^{\circ} + 36 0^{\circ} n + 10

x = \frac{324 0 ^{\circ} n + 72 0 ^{\circ} + 90}{27}, x = 18 0^{\circ} - 8 0^{\circ} + 36 0^{\circ} n + 10

作图

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