zs

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

受欢迎的三角函数 >

sin(5x-10)=cos(x-8)

解答

sin (5 x - 10) = cos (x - 8)

解答

x = \frac{4 πn + 36 + π}{12}, x = \frac{4 πn + 4 + π}{8}

+1

度数

x = 186.88733 \dots^{\circ} + 6 0^{\circ} n, x = 51.14788 \dots^{\circ} + 9 0^{\circ} n

求解步骤

sin (5 x - 10) = cos (x - 8)

使用三角恒等式改写

sin (5 x - 10) = cos (x - 8)

利用以下特性:

cos (x) = sin (\frac{π}{2} - x)

sin (5 x - 10) = sin (\frac{π}{2} - (x - 8))

sin (5 x - 10) = sin (\frac{π}{2} - (x - 8))

使用反三角函数性质

sin (5 x - 10) = sin (\frac{π}{2} - (x - 8))

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

5 x - 10 = \frac{π}{2} - (x - 8) + 2 πn, 5 x - 10 = π - (\frac{π}{2} - (x - 8)) + 2 πn

5 x - 10 = \frac{π}{2} - (x - 8) + 2 πn, 5 x - 10 = π - (\frac{π}{2} - (x - 8)) + 2 πn

5 x - 10 = \frac{π}{2} - (x - 8) + 2 πn : x = \frac{4 πn + 36 + π}{12}

5 x - 10 = \frac{π}{2} - (x - 8) + 2 πn

展开

\frac{π}{2} - (x - 8) + 2 πn : \frac{π}{2} - x + 8 + 2 πn

\frac{π}{2} - (x - 8) + 2 πn

- (x - 8) : - x + 8

- (x - 8)

打开括号

= - (x) - (- 8)

使用加减运算法则

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

= - x + 8

= \frac{π}{2} - x + 8 + 2 πn

5 x - 10 = \frac{π}{2} - x + 8 + 2 πn

将

10

到右边

5 x - 10 = \frac{π}{2} - x + 8 + 2 πn

两边加上

10

5 x - 10 + 10 = \frac{π}{2} - x + 8 + 2 πn + 10

化简

5 x - 10 + 10 = \frac{π}{2} - x + 8 + 2 πn + 10

化简

5 x - 10 + 10 : 5 x

5 x - 10 + 10

同类项相加:

- 10 + 10 = 0

= 5 x

化简

\frac{π}{2} - x + 8 + 2 πn + 10 : - x + 2 πn + 18 + \frac{π}{2}

\frac{π}{2} - x + 8 + 2 πn + 10

对同类项分组

= - x + 2 πn + \frac{π}{2} + 8 + 10

数字相加:

8 + 10 = 18

= - x + 2 πn + 18 + \frac{π}{2}

5 x = - x + 2 πn + 18 + \frac{π}{2}

5 x = - x + 2 πn + 18 + \frac{π}{2}

5 x = - x + 2 πn + 18 + \frac{π}{2}

将

x

para o lado esquerdo

5 x = - x + 2 πn + 18 + \frac{π}{2}

两边加上

x

5 x + x = - x + 2 πn + 18 + \frac{π}{2} + x

化简

6 x = 2 πn + 18 + \frac{π}{2}

6 x = 2 πn + 18 + \frac{π}{2}

两边除以

6

6 x = 2 πn + 18 + \frac{π}{2}

两边除以

6

\frac{6 x}{6} = \frac{2 πn}{6} + \frac{18}{6} + \frac{\frac{π}{2}}{6}

化简

\frac{6 x}{6} = \frac{2 πn}{6} + \frac{18}{6} + \frac{\frac{π}{2}}{6}

化简

\frac{6 x}{6} : x

\frac{6 x}{6}

数字相除:

\frac{6}{6} = 1

= x

化简

\frac{2 πn}{6} + \frac{18}{6} + \frac{\frac{π}{2}}{6} : \frac{4 πn + 36 + π}{12}

\frac{2 πn}{6} + \frac{18}{6} + \frac{\frac{π}{2}}{6}

使用法则

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

= \frac{2 πn + 18 + \frac{π}{2}}{6}

化简

2 πn + 18 + \frac{π}{2} : \frac{4 πn + 36 + π}{2}

2 πn + 18 + \frac{π}{2}

将项转换为分式:

2 πn = \frac{2 πn 2}{2}, 18 = \frac{18 \cdot 2}{2}

= \frac{2 πn \cdot 2}{2} + \frac{18 \cdot 2}{2} + \frac{π}{2}

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{2 πn \cdot 2 + 18 \cdot 2 + π}{2}

2 πn \cdot 2 + 18 \cdot 2 + π = 4 πn + 36 + π

2 πn \cdot 2 + 18 \cdot 2 + π

数字相乘:

2 \cdot 2 = 4

= 4 πn + 18 \cdot 2 + π

数字相乘:

18 \cdot 2 = 36

= 4 πn + 36 + π

= \frac{4 πn + 36 + π}{2}

= \frac{\frac{4 πn + 36 + π}{2}}{6}

使用分式法则:

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

= \frac{4 πn + 36 + π}{2 \cdot 6}

数字相乘:

2 \cdot 6 = 12

= \frac{4 πn + 36 + π}{12}

x = \frac{4 πn + 36 + π}{12}

x = \frac{4 πn + 36 + π}{12}

x = \frac{4 πn + 36 + π}{12}

5 x - 10 = π - (\frac{π}{2} - (x - 8)) + 2 πn : x = \frac{4 πn + 4 + π}{8}

5 x - 10 = π - (\frac{π}{2} - (x - 8)) + 2 πn

展开

π - (\frac{π}{2} - (x - 8)) + 2 πn : π - \frac{π}{2} + x - 8 + 2 πn

π - (\frac{π}{2} - (x - 8)) + 2 πn

- (x - 8) : - x + 8

- (x - 8)

打开括号

= - (x) - (- 8)

使用加减运算法则

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

= - x + 8

= π - (- x + 8 + \frac{π}{2}) + 2 πn

- (\frac{π}{2} - x + 8) : - \frac{π}{2} + x - 8

- (\frac{π}{2} - x + 8)

打开括号

= - (\frac{π}{2}) - (- x) - (8)

使用加减运算法则

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

= - \frac{π}{2} + x - 8

= π - \frac{π}{2} + x - 8 + 2 πn

5 x - 10 = π - \frac{π}{2} + x - 8 + 2 πn

将

10

到右边

5 x - 10 = π - \frac{π}{2} + x - 8 + 2 πn

两边加上

10

5 x - 10 + 10 = π - \frac{π}{2} + x - 8 + 2 πn + 10

化简

5 x - 10 + 10 = π - \frac{π}{2} + x - 8 + 2 πn + 10

化简

5 x - 10 + 10 : 5 x

5 x - 10 + 10

同类项相加:

- 10 + 10 = 0

= 5 x

化简

π - \frac{π}{2} + x - 8 + 2 πn + 10 : x + 2 πn + 2 + π - \frac{π}{2}

π - \frac{π}{2} + x - 8 + 2 πn + 10

对同类项分组

= x + π + 2 πn - \frac{π}{2} - 8 + 10

数字相加/相减:

- 8 + 10 = 2

= x + 2 πn + 2 + π - \frac{π}{2}

5 x = x + 2 πn + 2 + π - \frac{π}{2}

5 x = x + 2 πn + 2 + π - \frac{π}{2}

5 x = x + 2 πn + 2 + π - \frac{π}{2}

将

x

para o lado esquerdo

5 x = x + 2 πn + 2 + π - \frac{π}{2}

两边减去

x

5 x - x = x + 2 πn + 2 + π - \frac{π}{2} - x

化简

4 x = 2 πn + 2 + π - \frac{π}{2}

4 x = 2 πn + 2 + π - \frac{π}{2}

两边除以

4

4 x = 2 πn + 2 + π - \frac{π}{2}

两边除以

4

\frac{4 x}{4} = \frac{2 πn}{4} + \frac{2}{4} + \frac{π}{4} - \frac{\frac{π}{2}}{4}

化简

\frac{4 x}{4} = \frac{2 πn}{4} + \frac{2}{4} + \frac{π}{4} - \frac{\frac{π}{2}}{4}

化简

\frac{4 x}{4} : x

\frac{4 x}{4}

数字相除:

\frac{4}{4} = 1

= x

化简

\frac{2 πn}{4} + \frac{2}{4} + \frac{π}{4} - \frac{\frac{π}{2}}{4} : \frac{4 πn + 4 + π}{8}

\frac{2 πn}{4} + \frac{2}{4} + \frac{π}{4} - \frac{\frac{π}{2}}{4}

使用法则

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

= \frac{2 πn + 2 + π - \frac{π}{2}}{4}

化简

2 πn + 2 + π - \frac{π}{2} : \frac{4 πn + 4 + π}{2}

2 πn + 2 + π - \frac{π}{2}

将项转换为分式:

2 πn = \frac{2 πn 2}{2}, 2 = \frac{2 \cdot 2}{2}, π = \frac{π 2}{2}

= \frac{2 πn \cdot 2}{2} + \frac{2 \cdot 2}{2} + \frac{π 2}{2} - \frac{π}{2}

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{2 πn \cdot 2 + 2 \cdot 2 + π 2 - π}{2}

2 πn \cdot 2 + 2 \cdot 2 + π 2 - π = 4 πn + 4 + π

2 πn \cdot 2 + 2 \cdot 2 + π 2 - π

同类项相加:

2 π - π = π

= 2 \cdot 2 πn + 2 \cdot 2 + π

数字相乘:

2 \cdot 2 = 4

= 4 πn + 4 + π

= \frac{4 πn + 4 + π}{2}

= \frac{\frac{4 πn + 4 + π}{2}}{4}

使用分式法则:

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

= \frac{4 πn + 4 + π}{2 \cdot 4}

数字相乘:

2 \cdot 4 = 8

= \frac{4 πn + 4 + π}{8}

x = \frac{4 πn + 4 + π}{8}

x = \frac{4 πn + 4 + π}{8}

x = \frac{4 πn + 4 + π}{8}

x = \frac{4 πn + 36 + π}{12}, x = \frac{4 πn + 4 + π}{8}

x = \frac{4 πn + 36 + π}{12}, x = \frac{4 πn + 4 + π}{8}

作图

流行的例子

sin^2(x)+5sin(x)=3

sin^{2} (x) + 5 sin (x) = 3

14+7cos(2x)=21cos(x)

14 + 7 cos (2 x) = 21 cos (x)

sin(3x)=0,0<= x<2pi

sin (3 x) = 0, 0 \leq x < 2 π

sin(θ)=-1/5 ,pi<θ<(3pi)/2 ,cos(θ)

sin (θ) = - \frac{1}{5}, π < θ < \frac{3 π}{2}, cos (θ)

(sin(x))/(37)=(sin(30))/(30)

\frac{sin ( x )}{37} = \frac{sin ( 3 0 ^{\circ} )}{30}