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)=-cos(4x)

解答

sin (x) = - cos (4 x)

解答

x = \frac{π + 4 πn}{6}, x = - \frac{π + 4 πn}{10}

+1

度数

x = 3 0^{\circ} + 12 0^{\circ} n, x = - 1 8^{\circ} - 7 2^{\circ} n

求解步骤

sin (x) = - cos (4 x)

乘以

- 1

- sin (x) = cos (4 x)

使用三角恒等式改写

- sin (x) = cos (4 x)

利用以下特性:

- sin (x) = sin (- x)

sin (- (x)) = cos (4 x)

利用以下特性:

cos (x) = sin (\frac{π}{2} - x)

sin (- (x)) = sin (\frac{π}{2} - 4 x)

sin (- (x)) = sin (\frac{π}{2} - 4 x)

使用反三角函数性质

sin (- (x)) = sin (\frac{π}{2} - 4 x)

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

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

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

- (x) = \frac{π}{2} - 4 x + 2 πn : x = \frac{π + 4 πn}{6}

- (x) = \frac{π}{2} - 4 x + 2 πn

展开

- (x) : - x

- (x)

去除括号:

(a) = a

= - x

- x = \frac{π}{2} - 4 x + 2 πn

将

4 x

para o lado esquerdo

- x = \frac{π}{2} - 4 x + 2 πn

两边加上

4 x

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

化简

3 x = \frac{π}{2} + 2 πn

3 x = \frac{π}{2} + 2 πn

两边除以

3

3 x = \frac{π}{2} + 2 πn

两边除以

3

\frac{3 x}{3} = \frac{\frac{π}{2}}{3} + \frac{2 πn}{3}

化简

\frac{3 x}{3} = \frac{\frac{π}{2}}{3} + \frac{2 πn}{3}

化简

\frac{3 x}{3} : x

\frac{3 x}{3}

数字相除:

\frac{3}{3} = 1

= x

化简

\frac{\frac{π}{2}}{3} + \frac{2 πn}{3} : \frac{π + 4 πn}{6}

\frac{\frac{π}{2}}{3} + \frac{2 πn}{3}

使用法则

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

= \frac{\frac{π}{2} + 2 πn}{3}

化简

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

\frac{π}{2} + 2 πn

将项转换为分式:

2 πn = \frac{2 πn 2}{2}

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

数字相乘:

2 \cdot 2 = 4

= \frac{π + 4 πn}{2}

= \frac{\frac{π + 4 πn}{2}}{3}

使用分式法则:

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

= \frac{π + 4 πn}{2 \cdot 3}

数字相乘:

2 \cdot 3 = 6

= \frac{π + 4 πn}{6}

x = \frac{π + 4 πn}{6}

x = \frac{π + 4 πn}{6}

x = \frac{π + 4 πn}{6}

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

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

展开

- (x) : - x

- (x)

去除括号:

(a) = a

= - x

展开

π - (\frac{π}{2} - 4 x) + 2 πn : π - \frac{π}{2} + 4 x + 2 πn

π - (\frac{π}{2} - 4 x) + 2 πn

- (\frac{π}{2} - 4 x) : - \frac{π}{2} + 4 x

- (\frac{π}{2} - 4 x)

打开括号

= - (\frac{π}{2}) - (- 4 x)

使用加减运算法则

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

= - \frac{π}{2} + 4 x

= π - \frac{π}{2} + 4 x + 2 πn

- x = π - \frac{π}{2} + 4 x + 2 πn

将

4 x

para o lado esquerdo

- x = π - \frac{π}{2} + 4 x + 2 πn

两边减去

4 x

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

化简

- 5 x = π - \frac{π}{2} + 2 πn

- 5 x = π - \frac{π}{2} + 2 πn

两边除以

- 5

- 5 x = π - \frac{π}{2} + 2 πn

两边除以

- 5

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

化简

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

化简

\frac{- 5 x}{- 5} : x

\frac{- 5 x}{- 5}

使用分式法则:

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

= \frac{5 x}{5}

数字相除:

\frac{5}{5} = 1

= x

化简

\frac{π}{- 5} - \frac{\frac{π}{2}}{- 5} + \frac{2 πn}{- 5} : - \frac{π + 4 πn}{10}

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

使用法则

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

= \frac{π - \frac{π}{2} + 2 πn}{- 5}

使用分式法则:

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

= - \frac{π - \frac{π}{2} + 2 πn}{5}

化简

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

π - \frac{π}{2} + 2 πn

将项转换为分式:

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

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

π 2 - π + 2 πn \cdot 2 = π + 4 πn

π 2 - π + 2 πn \cdot 2

同类项相加:

2 π - π = π

= π + 2 \cdot 2 πn

数字相乘:

2 \cdot 2 = 4

= π + 4 πn

= \frac{π + 4 πn}{2}

= - \frac{\frac{π + 4 πn}{2}}{5}

化简

\frac{\frac{π + 4 πn}{2}}{5} : \frac{π + 4 πn}{10}

\frac{\frac{π + 4 πn}{2}}{5}

使用分式法则:

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

= \frac{π + 4 πn}{2 \cdot 5}

数字相乘:

2 \cdot 5 = 10

= \frac{π + 4 πn}{10}

= - \frac{π + 4 πn}{10}

x = - \frac{π + 4 πn}{10}

x = - \frac{π + 4 πn}{10}

x = - \frac{π + 4 πn}{10}

x = \frac{π + 4 πn}{6}, x = - \frac{π + 4 πn}{10}

x = \frac{π + 4 πn}{6}, x = - \frac{π + 4 πn}{10}

作图

流行的例子

cos(θ)= 2/(3sqrt(38))

cos (θ) = \frac{2}{3 38}

cos(2θ)= 20/29

cos (2 θ) = \frac{20}{29}

sin(x)=(sqrt(2))/4

sin (x) = \frac{2}{4}

2 tan (2 x) - 6 = 0

8sin(θ)+15cos(θ)=18

8 sin (θ) + 15 cos (θ) = 18