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受欢迎的三角函数 >

sin(x-20)=cos(x)

解答

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

解答

x = - 36 0^{\circ} n + 5 5^{\circ}, x = - 12 5^{\circ} - 36 0^{\circ} n

+1

弧度

x = \frac{11 π}{36} - 2 πn, x = - \frac{25 π}{36} - 2 πn

求解步骤

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

两边减去

cos (x)

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

使用三角恒等式改写

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

利用以下特性:

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

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

乘开

9 0^{\circ} - (- 2 0^{\circ} + x) : - x + 11 0^{\circ}

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

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

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

打开括号

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

使用加减运算法则

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

= 2 0^{\circ} - x

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

化简

9 0^{\circ} + 2 0^{\circ} - x : - x + 11 0^{\circ}

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

2, 9

的最小公倍数:

18

2, 9

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

9

质因数分解:

3 \cdot 3

9

9

除以

39 = 3 \cdot 3

= 3 \cdot 3

将每个因子乘以它在

2

或

9

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}

对于

2 0^{\circ} :

将分母和分子乘以

2

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

= 9 0^{\circ} + 2 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} 2}{18}

同类项相加:

162 0^{\circ} + 36 0^{\circ} = 198 0^{\circ}

= - x + 11 0^{\circ}

= - x + 11 0^{\circ}

= - cos (x) + cos (- x + 11 0^{\circ})

使用和差化积恒等式:

cos (s) - cos (t) = - 2 sin (\frac{s + t}{2}) sin (\frac{s - t}{2})

= - 2 sin (\frac{11 0 ^{\circ} - x + x}{2}) sin (\frac{11 0 ^{\circ} - x - x}{2})

化简

- 2 sin (\frac{11 0 ^{\circ} - x + x}{2}) sin (\frac{11 0 ^{\circ} - x - x}{2}) : - 2 sin (5 5^{\circ}) sin (\frac{198 0 ^{\circ} - 36 x}{36})

- 2 sin (\frac{11 0 ^{\circ} - x + x}{2}) sin (\frac{11 0 ^{\circ} - x - x}{2})

\frac{11 0 ^{\circ} - x + x}{2} = 5 5^{\circ}

\frac{11 0 ^{\circ} - x + x}{2}

同类项相加:

- x + x = 0

= \frac{11 0 ^{\circ}}{2}

使用分式法则:

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

= \frac{198 0 ^{\circ}}{18 \cdot 2}

数字相乘:

18 \cdot 2 = 36

= 5 5^{\circ}

= - 2 sin (5 5^{\circ}) sin (\frac{- x - x + 11 0 ^{\circ}}{2})

\frac{11 0 ^{\circ} - x - x}{2} = \frac{198 0 ^{\circ} - 36 x}{36}

\frac{11 0 ^{\circ} - x - x}{2}

同类项相加:

- x - x = - 2 x

= \frac{11 0 ^{\circ} - 2 x}{2}

化简

11 0^{\circ} - 2 x : \frac{198 0 ^{\circ} - 36 x}{18}

11 0^{\circ} - 2 x

将项转换为分式:

2 x = \frac{2 x 18}{18}

= 11 0^{\circ} - \frac{2 x \cdot 18}{18}

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{198 0 ^{\circ} - 2 x \cdot 18}{18}

数字相乘:

2 \cdot 18 = 36

= \frac{198 0 ^{\circ} - 36 x}{18}

= \frac{\frac{198 0 ^{\circ} - 36 x}{18}}{2}

使用分式法则:

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

= \frac{198 0 ^{\circ} - 36 x}{18 \cdot 2}

数字相乘:

18 \cdot 2 = 36

= \frac{198 0 ^{\circ} - 36 x}{36}

= - 2 sin (5 5^{\circ}) sin (\frac{- 36 x + 198 0 ^{\circ}}{36})

= - 2 sin (5 5^{\circ}) sin (\frac{198 0 ^{\circ} - 36 x}{36})

- 2 sin (5 5^{\circ}) sin (\frac{198 0 ^{\circ} - 36 x}{36}) = 0

两边除以

- 2 sin (5 5^{\circ})

- 2 sin (5 5^{\circ}) sin (\frac{198 0 ^{\circ} - 36 x}{36}) = 0

两边除以

- 2 sin (5 5^{\circ})

\frac{- 2 sin ( 5 5 ^{\circ} ) sin ( \frac{198 0 ^{\circ} - 36 x}{36} )}{- 2 sin ( 5 5 ^{\circ} )} = \frac{0}{- 2 sin ( 5 5 ^{\circ} )}

化简

sin (\frac{198 0 ^{\circ} - 36 x}{36}) = 0

sin (\frac{198 0 ^{\circ} - 36 x}{36}) = 0

sin (\frac{198 0 ^{\circ} - 36 x}{36}) = 0

的通解

sin (x)

周期表（周期为

36 0^{\circ} n

"）：

x 0 3 0^{\circ} 4 5^{\circ} 6 0^{\circ} 9 0^{\circ} 12 0^{\circ} 13 5^{\circ} 15 0^{\circ} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} x 18 0^{\circ} 21 0^{\circ} 22 5^{\circ} 24 0^{\circ} 27 0^{\circ} 30 0^{\circ} 31 5^{\circ} 33 0^{\circ} sin (x) 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2}

\frac{198 0 ^{\circ} - 36 x}{36} = 0 + 36 0^{\circ} n, \frac{198 0 ^{\circ} - 36 x}{36} = 18 0^{\circ} + 36 0^{\circ} n

\frac{198 0 ^{\circ} - 36 x}{36} = 0 + 36 0^{\circ} n, \frac{198 0 ^{\circ} - 36 x}{36} = 18 0^{\circ} + 36 0^{\circ} n

解

\frac{198 0 ^{\circ} - 36 x}{36} = 0 + 36 0^{\circ} n : x = - 36 0^{\circ} n + 5 5^{\circ}

\frac{198 0 ^{\circ} - 36 x}{36} = 0 + 36 0^{\circ} n

0 + 36 0^{\circ} n = 36 0^{\circ} n

\frac{198 0 ^{\circ} - 36 x}{36} = 36 0^{\circ} n

在两边乘以

36

\frac{198 0 ^{\circ} - 36 x}{36} = 36 0^{\circ} n

在两边乘以

36

\frac{36 ( 198 0 ^{\circ} - 36 x )}{36} = 36 \cdot 36 0^{\circ} n

化简

198 0^{\circ} - 36 x = 1296 0^{\circ} n

198 0^{\circ} - 36 x = 1296 0^{\circ} n

将

198 0^{\circ}

到右边

198 0^{\circ} - 36 x = 1296 0^{\circ} n

两边减去

198 0^{\circ}

198 0^{\circ} - 36 x - 198 0^{\circ} = 1296 0^{\circ} n - 198 0^{\circ}

化简

- 36 x = 1296 0^{\circ} n - 198 0^{\circ}

- 36 x = 1296 0^{\circ} n - 198 0^{\circ}

两边除以

- 36

- 36 x = 1296 0^{\circ} n - 198 0^{\circ}

两边除以

- 36

\frac{- 36 x}{- 36} = \frac{1296 0 ^{\circ} n}{- 36} - \frac{198 0 ^{\circ}}{- 36}

化简

\frac{- 36 x}{- 36} = \frac{1296 0 ^{\circ} n}{- 36} - \frac{198 0 ^{\circ}}{- 36}

化简

\frac{- 36 x}{- 36} : x

\frac{- 36 x}{- 36}

使用分式法则:

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

= \frac{36 x}{36}

数字相除:

\frac{36}{36} = 1

= x

化简

\frac{1296 0 ^{\circ} n}{- 36} - \frac{198 0 ^{\circ}}{- 36} : - 36 0^{\circ} n + 5 5^{\circ}

\frac{1296 0 ^{\circ} n}{- 36} - \frac{198 0 ^{\circ}}{- 36}

\frac{1296 0 ^{\circ} n}{- 36} = - 36 0^{\circ} n

\frac{1296 0 ^{\circ} n}{- 36}

使用分式法则:

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

= - \frac{1296 0 ^{\circ} n}{36}

数字相除:

\frac{72}{36} = 2

= - 36 0^{\circ} n

= - 36 0^{\circ} n - \frac{198 0 ^{\circ}}{- 36}

使用分式法则:

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

= - 36 0^{\circ} n - (- 5 5^{\circ})

使用法则

- (- a) = a

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

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

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

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

解

\frac{198 0 ^{\circ} - 36 x}{36} = 18 0^{\circ} + 36 0^{\circ} n : x = - 12 5^{\circ} - 36 0^{\circ} n

\frac{198 0 ^{\circ} - 36 x}{36} = 18 0^{\circ} + 36 0^{\circ} n

在两边乘以

36

\frac{198 0 ^{\circ} - 36 x}{36} = 18 0^{\circ} + 36 0^{\circ} n

在两边乘以

36

\frac{36 ( 198 0 ^{\circ} - 36 x )}{36} = 648 0^{\circ} + 36 \cdot 36 0^{\circ} n

化简

198 0^{\circ} - 36 x = 648 0^{\circ} + 1296 0^{\circ} n

198 0^{\circ} - 36 x = 648 0^{\circ} + 1296 0^{\circ} n

将

198 0^{\circ}

到右边

198 0^{\circ} - 36 x = 648 0^{\circ} + 1296 0^{\circ} n

两边减去

198 0^{\circ}

198 0^{\circ} - 36 x - 198 0^{\circ} = 648 0^{\circ} + 1296 0^{\circ} n - 198 0^{\circ}

化简

- 36 x = 450 0^{\circ} + 1296 0^{\circ} n

- 36 x = 450 0^{\circ} + 1296 0^{\circ} n

两边除以

- 36

- 36 x = 450 0^{\circ} + 1296 0^{\circ} n

两边除以

- 36

\frac{- 36 x}{- 36} = \frac{450 0 ^{\circ}}{- 36} + \frac{1296 0 ^{\circ} n}{- 36}

化简

\frac{- 36 x}{- 36} = \frac{450 0 ^{\circ}}{- 36} + \frac{1296 0 ^{\circ} n}{- 36}

化简

\frac{- 36 x}{- 36} : x

\frac{- 36 x}{- 36}

使用分式法则:

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

= \frac{36 x}{36}

数字相除:

\frac{36}{36} = 1

= x

化简

\frac{450 0 ^{\circ}}{- 36} + \frac{1296 0 ^{\circ} n}{- 36} : - 12 5^{\circ} - 36 0^{\circ} n

\frac{450 0 ^{\circ}}{- 36} + \frac{1296 0 ^{\circ} n}{- 36}

使用分式法则:

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

= - 12 5^{\circ} + \frac{1296 0 ^{\circ} n}{- 36}

\frac{1296 0 ^{\circ} n}{- 36} = - 36 0^{\circ} n

\frac{1296 0 ^{\circ} n}{- 36}

使用分式法则:

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

= - \frac{1296 0 ^{\circ} n}{36}

数字相除:

\frac{72}{36} = 2

= - 36 0^{\circ} n

= - 12 5^{\circ} - 36 0^{\circ} n

x = - 12 5^{\circ} - 36 0^{\circ} n

x = - 12 5^{\circ} - 36 0^{\circ} n

x = - 12 5^{\circ} - 36 0^{\circ} n

x = - 36 0^{\circ} n + 5 5^{\circ}, x = - 12 5^{\circ} - 36 0^{\circ} n

作图

流行的例子

cos(x)+cos(5x)=0

cos (x) + cos (5 x) = 0

7cos(t)+5sin(t)=0

7 cos (t) + 5 sin (t) = 0

cos (X) = 0.4848

pi/3 =3+2sin(2t)

\frac{π}{3} = 3 + 2 sin (2 t)

1+sin(2x)=5(sin(x)+cos(x))

1 + sin (2 x) = 5 (sin (x) + cos (x))