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(x+37)=cos(2x+8)

解答

sin (x + 3 7^{\circ}) = cos (2 x + 8)

解答

x = \frac{6480 0 ^{\circ} n + 954 0 ^{\circ} - 1440}{540}, x = - \frac{954 0 ^{\circ} + 6480 0 ^{\circ} n + 1440}{180}

+1

弧度

x = \frac{\frac{53 π}{5}}{108} - \frac{8}{3} + \frac{360 π}{540} n, x = - 8 - \frac{\frac{53 π}{5}}{36} - \frac{360 π}{180} n

求解步骤

sin (x + 3 7^{\circ}) = cos (2 x + 8)

使用三角恒等式改写

sin (x + 3 7^{\circ}) = cos (2 x + 8)

利用以下特性:

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

sin (x + 3 7^{\circ}) = sin (9 0^{\circ} - (2 x + 8))

sin (x + 3 7^{\circ}) = sin (9 0^{\circ} - (2 x + 8))

使用反三角函数性质

sin (x + 3 7^{\circ}) = sin (9 0^{\circ} - (2 x + 8))

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

x + 3 7^{\circ} = 9 0^{\circ} - (2 x + 8) + 36 0^{\circ} n, x + 3 7^{\circ} = 18 0^{\circ} - (9 0^{\circ} - (2 x + 8)) + 36 0^{\circ} n

x + 3 7^{\circ} = 9 0^{\circ} - (2 x + 8) + 36 0^{\circ} n, x + 3 7^{\circ} = 18 0^{\circ} - (9 0^{\circ} - (2 x + 8)) + 36 0^{\circ} n

x + 3 7^{\circ} = 9 0^{\circ} - (2 x + 8) + 36 0^{\circ} n : x = \frac{6480 0 ^{\circ} n + 954 0 ^{\circ} - 1440}{540}

x + 3 7^{\circ} = 9 0^{\circ} - (2 x + 8) + 36 0^{\circ} n

展开

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

9 0^{\circ} - (2 x + 8) + 36 0^{\circ} n

- (2 x + 8) : - 2 x - 8

- (2 x + 8)

打开括号

= - (2 x) - (8)

使用加减运算法则

+ (- a) = - a

= - 2 x - 8

= 9 0^{\circ} - 2 x - 8 + 36 0^{\circ} n

x + 3 7^{\circ} = 9 0^{\circ} - 2 x - 8 + 36 0^{\circ} n

将

3 7^{\circ}

到右边

x + 3 7^{\circ} = 9 0^{\circ} - 2 x - 8 + 36 0^{\circ} n

两边减去

3 7^{\circ}

x + 3 7^{\circ} - 3 7^{\circ} = 9 0^{\circ} - 2 x - 8 + 36 0^{\circ} n - 3 7^{\circ}

化简

x + 3 7^{\circ} - 3 7^{\circ} = 9 0^{\circ} - 2 x - 8 + 36 0^{\circ} n - 3 7^{\circ}

化简

x + 3 7^{\circ} - 3 7^{\circ} : x

x + 3 7^{\circ} - 3 7^{\circ}

同类项相加:

3 7^{\circ} - 3 7^{\circ} = 0

= x

化简

9 0^{\circ} - 2 x - 8 + 36 0^{\circ} n - 3 7^{\circ} : - 2 x + 36 0^{\circ} n + 5 3^{\circ} - 8

9 0^{\circ} - 2 x - 8 + 36 0^{\circ} n - 3 7^{\circ}

对同类项分组

= - 2 x + 36 0^{\circ} n + 9 0^{\circ} - 3 7^{\circ} - 8

合并分式

9 0^{\circ} - 3 7^{\circ} : 5 3^{\circ}

9 0^{\circ} - 3 7^{\circ}

2, 180

的最小公倍数:

180

2, 180

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

180

质因数分解:

2 \cdot 2 \cdot 3 \cdot 3 \cdot 5

180

180

除以

2180 = 90 \cdot 2

= 2 \cdot 90

90

除以

290 = 45 \cdot 2

= 2 \cdot 2 \cdot 45

45

除以

345 = 15 \cdot 3

= 2 \cdot 2 \cdot 3 \cdot 15

15

除以

315 = 5 \cdot 3

= 2 \cdot 2 \cdot 3 \cdot 3 \cdot 5

2, 3, 5

都是质数，因此无法进一步因数分解

= 2 \cdot 2 \cdot 3 \cdot 3 \cdot 5

将每个因子乘以它在

2

或

180

中出现的最多次数

= 2 \cdot 2 \cdot 3 \cdot 3 \cdot 5

数字相乘:

2 \cdot 2 \cdot 3 \cdot 3 \cdot 5 = 180

= 180

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

180

对于

9 0^{\circ} :

将分母和分子乘以

90

9 0^{\circ} = \frac{18 0 ^{\circ} 90}{2 \cdot 90} = 9 0^{\circ}

= 9 0^{\circ} - 3 7^{\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} 90 - 666 0 ^{\circ}}{180}

同类项相加:

1620 0^{\circ} - 666 0^{\circ} = 954 0^{\circ}

= 5 3^{\circ}

= - 2 x + 36 0^{\circ} n + 5 3^{\circ} - 8

x = - 2 x + 36 0^{\circ} n + 5 3^{\circ} - 8

x = - 2 x + 36 0^{\circ} n + 5 3^{\circ} - 8

x = - 2 x + 36 0^{\circ} n + 5 3^{\circ} - 8

将

2 x

para o lado esquerdo

x = - 2 x + 36 0^{\circ} n + 5 3^{\circ} - 8

两边加上

2 x

x + 2 x = - 2 x + 36 0^{\circ} n + 5 3^{\circ} - 8 + 2 x

化简

3 x = 36 0^{\circ} n + 5 3^{\circ} - 8

3 x = 36 0^{\circ} n + 5 3^{\circ} - 8

两边除以

3

3 x = 36 0^{\circ} n + 5 3^{\circ} - 8

两边除以

3

\frac{3 x}{3} = \frac{36 0 ^{\circ} n}{3} + \frac{5 3 ^{\circ}}{3} - \frac{8}{3}

化简

\frac{3 x}{3} = \frac{36 0 ^{\circ} n}{3} + \frac{5 3 ^{\circ}}{3} - \frac{8}{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{5 3 ^{\circ}}{3} - \frac{8}{3} : \frac{6480 0 ^{\circ} n + 954 0 ^{\circ} - 1440}{540}

\frac{36 0 ^{\circ} n}{3} + \frac{5 3 ^{\circ}}{3} - \frac{8}{3}

使用法则

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

= \frac{36 0 ^{\circ} n + 5 3 ^{\circ} - 8}{3}

化简

36 0^{\circ} n + 5 3^{\circ} - 8 : \frac{6480 0 ^{\circ} n + 954 0 ^{\circ} - 1440}{180}

36 0^{\circ} n + 5 3^{\circ} - 8

将项转换为分式:

36 0^{\circ} n = \frac{36 0 ^{\circ} n 180}{180}, 8 = \frac{8 \cdot 180}{180}

= \frac{36 0 ^{\circ} n \cdot 180}{180} + 5 3^{\circ} - \frac{8 \cdot 180}{180}

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 180 + 954 0 ^{\circ} - 8 \cdot 180}{180}

36 0^{\circ} n \cdot 180 + 954 0^{\circ} - 8 \cdot 180 = 6480 0^{\circ} n + 954 0^{\circ} - 1440

36 0^{\circ} n \cdot 180 + 954 0^{\circ} - 8 \cdot 180

数字相乘:

2 \cdot 180 = 360

= 6480 0^{\circ} n + 954 0^{\circ} - 8 \cdot 180

数字相乘:

8 \cdot 180 = 1440

= 6480 0^{\circ} n + 954 0^{\circ} - 1440

= \frac{6480 0 ^{\circ} n + 954 0 ^{\circ} - 1440}{180}

= \frac{\frac{6480 0 ^{\circ} n + 954 0 ^{\circ} - 1440}{180}}{3}

使用分式法则:

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

= \frac{6480 0 ^{\circ} n + 954 0 ^{\circ} - 1440}{180 \cdot 3}

数字相乘:

180 \cdot 3 = 540

= \frac{6480 0 ^{\circ} n + 954 0 ^{\circ} - 1440}{540}

x = \frac{6480 0 ^{\circ} n + 954 0 ^{\circ} - 1440}{540}

x = \frac{6480 0 ^{\circ} n + 954 0 ^{\circ} - 1440}{540}

x = \frac{6480 0 ^{\circ} n + 954 0 ^{\circ} - 1440}{540}

x + 3 7^{\circ} = 18 0^{\circ} - (9 0^{\circ} - (2 x + 8)) + 36 0^{\circ} n : x = - \frac{954 0 ^{\circ} + 6480 0 ^{\circ} n + 1440}{180}

x + 3 7^{\circ} = 18 0^{\circ} - (9 0^{\circ} - (2 x + 8)) + 36 0^{\circ} n

展开

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

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

- (2 x + 8) : - 2 x - 8

- (2 x + 8)

打开括号

= - (2 x) - (8)

使用加减运算法则

+ (- a) = - a

= - 2 x - 8

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

- (9 0^{\circ} - 2 x - 8) : - 9 0^{\circ} + 2 x + 8

- (9 0^{\circ} - 2 x - 8)

打开括号

= - (9 0^{\circ}) - (- 2 x) - (- 8)

使用加减运算法则

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

= - 9 0^{\circ} + 2 x + 8

= 18 0^{\circ} - 9 0^{\circ} + 2 x + 8 + 36 0^{\circ} n

x + 3 7^{\circ} = 18 0^{\circ} - 9 0^{\circ} + 2 x + 8 + 36 0^{\circ} n

将

3 7^{\circ}

到右边

x + 3 7^{\circ} = 18 0^{\circ} - 9 0^{\circ} + 2 x + 8 + 36 0^{\circ} n

两边减去

3 7^{\circ}

x + 3 7^{\circ} - 3 7^{\circ} = 18 0^{\circ} - 9 0^{\circ} + 2 x + 8 + 36 0^{\circ} n - 3 7^{\circ}

化简

x + 3 7^{\circ} - 3 7^{\circ} = 18 0^{\circ} - 9 0^{\circ} + 2 x + 8 + 36 0^{\circ} n - 3 7^{\circ}

化简

x + 3 7^{\circ} - 3 7^{\circ} : x

x + 3 7^{\circ} - 3 7^{\circ}

同类项相加:

3 7^{\circ} - 3 7^{\circ} = 0

= x

化简

18 0^{\circ} - 9 0^{\circ} + 2 x + 8 + 36 0^{\circ} n - 3 7^{\circ} : 2 x + 18 0^{\circ} + 36 0^{\circ} n - 12 7^{\circ} + 8

18 0^{\circ} - 9 0^{\circ} + 2 x + 8 + 36 0^{\circ} n - 3 7^{\circ}

对同类项分组

= 2 x + 18 0^{\circ} + 36 0^{\circ} n - 9 0^{\circ} - 3 7^{\circ} + 8

合并分式

- 9 0^{\circ} - 3 7^{\circ} : - 12 7^{\circ}

- 9 0^{\circ} - 3 7^{\circ}

2, 180

的最小公倍数:

180

2, 180

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

180

质因数分解:

2 \cdot 2 \cdot 3 \cdot 3 \cdot 5

180

180

除以

2180 = 90 \cdot 2

= 2 \cdot 90

90

除以

290 = 45 \cdot 2

= 2 \cdot 2 \cdot 45

45

除以

345 = 15 \cdot 3

= 2 \cdot 2 \cdot 3 \cdot 15

15

除以

315 = 5 \cdot 3

= 2 \cdot 2 \cdot 3 \cdot 3 \cdot 5

2, 3, 5

都是质数，因此无法进一步因数分解

= 2 \cdot 2 \cdot 3 \cdot 3 \cdot 5

将每个因子乘以它在

2

或

180

中出现的最多次数

= 2 \cdot 2 \cdot 3 \cdot 3 \cdot 5

数字相乘:

2 \cdot 2 \cdot 3 \cdot 3 \cdot 5 = 180

= 180

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

180

对于

9 0^{\circ} :

将分母和分子乘以

90

9 0^{\circ} = \frac{18 0 ^{\circ} 90}{2 \cdot 90} = 9 0^{\circ}

= - 9 0^{\circ} - 3 7^{\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} 90 - 666 0 ^{\circ}}{180}

同类项相加:

- 1620 0^{\circ} - 666 0^{\circ} = - 2286 0^{\circ}

= \frac{- 2286 0 ^{\circ}}{180}

使用分式法则:

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

= - 12 7^{\circ}

= 2 x + 18 0^{\circ} + 36 0^{\circ} n - 12 7^{\circ} + 8

x = 2 x + 18 0^{\circ} + 36 0^{\circ} n - 12 7^{\circ} + 8

x = 2 x + 18 0^{\circ} + 36 0^{\circ} n - 12 7^{\circ} + 8

x = 2 x + 18 0^{\circ} + 36 0^{\circ} n - 12 7^{\circ} + 8

将

2 x

para o lado esquerdo

x = 2 x + 18 0^{\circ} + 36 0^{\circ} n - 12 7^{\circ} + 8

两边减去

2 x

x - 2 x = 2 x + 18 0^{\circ} + 36 0^{\circ} n - 12 7^{\circ} + 8 - 2 x

化简

- x = 18 0^{\circ} + 36 0^{\circ} n - 12 7^{\circ} + 8

- x = 18 0^{\circ} + 36 0^{\circ} n - 12 7^{\circ} + 8

两边除以

- 1

- x = 18 0^{\circ} + 36 0^{\circ} n - 12 7^{\circ} + 8

两边除以

- 1

\frac{- x}{- 1} = \frac{18 0 ^{\circ}}{- 1} + \frac{36 0 ^{\circ} n}{- 1} - \frac{12 7 ^{\circ}}{- 1} + \frac{8}{- 1}

化简

\frac{- x}{- 1} = \frac{18 0 ^{\circ}}{- 1} + \frac{36 0 ^{\circ} n}{- 1} - \frac{12 7 ^{\circ}}{- 1} + \frac{8}{- 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{12 7 ^{\circ}}{- 1} + \frac{8}{- 1} : - \frac{954 0 ^{\circ} + 6480 0 ^{\circ} n + 1440}{180}

\frac{18 0 ^{\circ}}{- 1} + \frac{36 0 ^{\circ} n}{- 1} - \frac{12 7 ^{\circ}}{- 1} + \frac{8}{- 1}

对同类项分组

= \frac{18 0 ^{\circ}}{- 1} + \frac{8}{- 1} + \frac{36 0 ^{\circ} n}{- 1} - \frac{12 7 ^{\circ}}{- 1}

使用法则

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

= \frac{18 0 ^{\circ} + 8 + 36 0 ^{\circ} n - 12 7 ^{\circ}}{- 1}

使用分式法则:

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

= - \frac{18 0 ^{\circ} + 8 + 36 0 ^{\circ} n - 12 7 ^{\circ}}{1}

化简

18 0^{\circ} + 8 + 36 0^{\circ} n - 12 7^{\circ} : \frac{954 0 ^{\circ} + 6480 0 ^{\circ} n + 1440}{180}

18 0^{\circ} + 8 + 36 0^{\circ} n - 12 7^{\circ}

将项转换为分式:

18 0^{\circ} = 18 0^{\circ}, 8 = \frac{8 \cdot 180}{180}, 36 0^{\circ} n = \frac{36 0 ^{\circ} n 180}{180}

= 18 0^{\circ} + \frac{8 \cdot 180}{180} + \frac{36 0 ^{\circ} n \cdot 180}{180} - 12 7^{\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} 180 + 8 \cdot 180 + 36 0 ^{\circ} n \cdot 180 - 2286 0 ^{\circ}}{180}

18 0^{\circ} 180 + 8 \cdot 180 + 36 0^{\circ} n \cdot 180 - 2286 0^{\circ} = 954 0^{\circ} + 6480 0^{\circ} n + 1440

18 0^{\circ} 180 + 8 \cdot 180 + 36 0^{\circ} n \cdot 180 - 2286 0^{\circ}

对同类项分组

= 3240 0^{\circ} - 2286 0^{\circ} + 2 \cdot 3240 0^{\circ} n + 8 \cdot 180

同类项相加:

3240 0^{\circ} - 2286 0^{\circ} = 954 0^{\circ}

= 954 0^{\circ} + 2 \cdot 3240 0^{\circ} n + 8 \cdot 180

数字相乘:

2 \cdot 180 = 360

= 954 0^{\circ} + 6480 0^{\circ} n + 8 \cdot 180

数字相乘:

8 \cdot 180 = 1440

= 954 0^{\circ} + 6480 0^{\circ} n + 1440

= \frac{954 0 ^{\circ} + 6480 0 ^{\circ} n + 1440}{180}

= - \frac{\frac{954 0 ^{\circ} + 6480 0 ^{\circ} n + 1440}{180}}{1}

使用分式法则:

\frac{a}{1} = a

= - \frac{954 0 ^{\circ} + 6480 0 ^{\circ} n + 1440}{180}

x = - \frac{954 0 ^{\circ} + 6480 0 ^{\circ} n + 1440}{180}

x = - \frac{954 0 ^{\circ} + 6480 0 ^{\circ} n + 1440}{180}

x = - \frac{954 0 ^{\circ} + 6480 0 ^{\circ} n + 1440}{180}

x = \frac{6480 0 ^{\circ} n + 954 0 ^{\circ} - 1440}{540}, x = - \frac{954 0 ^{\circ} + 6480 0 ^{\circ} n + 1440}{180}

x = \frac{6480 0 ^{\circ} n + 954 0 ^{\circ} - 1440}{540}, x = - \frac{954 0 ^{\circ} + 6480 0 ^{\circ} n + 1440}{180}

作图

流行的例子

cos^{2} (5 x) = 1

3sin^2(x)=9cos^2(x)

3 sin^{2} (x) = 9 cos^{2} (x)

3cos^2(x)-3=sin(x)

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

1+cos(x)=sin^2(x)

1 + cos (x) = sin^{2} (x)

tan(x-pi/2)= 1/(sqrt(3))

tan (x - \frac{π}{2}) = \frac{1}{3}