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受欢迎的三角函数 >

tan(x+32)=cot(x-20)

解答

tan (x + 3 2^{\circ}) = cot (x - 2 0^{\circ})

解答

x = 3 9^{\circ} + 18 0^{\circ} n, x = 12 9^{\circ} + 18 0^{\circ} n

+1

弧度

x = \frac{13 π}{60} + πn, x = \frac{43 π}{60} + πn

求解步骤

tan (x + 3 2^{\circ}) = cot (x - 2 0^{\circ})

两边减去

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

tan (x + 3 2^{\circ}) - cot (x - 2 0^{\circ}) = 0

化简

tan (x + 3 2^{\circ}) - cot (x - 2 0^{\circ}) : tan (\frac{45 x + 144 0 ^{\circ}}{45}) - cot (\frac{9 x - 18 0 ^{\circ}}{9})

tan (x + 3 2^{\circ}) - cot (x - 2 0^{\circ})

化简

x + 3 2^{\circ} : \frac{45 x + 144 0 ^{\circ}}{45}

x + 3 2^{\circ}

将项转换为分式:

x = \frac{x 45}{45}

= \frac{x \cdot 45}{45} + 3 2^{\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{x \cdot 45 + 144 0 ^{\circ}}{45}

= tan (\frac{45 x + 144 0 ^{\circ}}{45}) - cot (x - 2 0^{\circ})

化简

x - 2 0^{\circ} : \frac{9 x - 18 0 ^{\circ}}{9}

x - 2 0^{\circ}

将项转换为分式:

x = \frac{x 9}{9}

= \frac{x \cdot 9}{9} - 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{x \cdot 9 - 18 0 ^{\circ}}{9}

= tan (\frac{45 x + 144 0 ^{\circ}}{45}) - cot (\frac{9 x - 18 0 ^{\circ}}{9})

tan (\frac{45 x + 144 0 ^{\circ}}{45}) - cot (\frac{9 x - 18 0 ^{\circ}}{9}) = 0

用 sin, cos 表示

- cot (\frac{- 18 0 ^{\circ} + 9 x}{9}) + tan (\frac{45 x + 144 0 ^{\circ}}{45})

使用基本三角恒等式:

cot (x) = \frac{cos ( x )}{sin ( x )}

= - \frac{cos ( \frac{- 18 0 ^{\circ} + 9 x}{9} )}{sin ( \frac{- 18 0 ^{\circ} + 9 x}{9} )} + tan (\frac{45 x + 144 0 ^{\circ}}{45})

使用基本三角恒等式:

tan (x) = \frac{sin ( x )}{cos ( x )}

= - \frac{cos ( \frac{- 18 0 ^{\circ} + 9 x}{9} )}{sin ( \frac{- 18 0 ^{\circ} + 9 x}{9} )} + \frac{sin ( \frac{45 x + 144 0 ^{\circ}}{45} )}{cos ( \frac{45 x + 144 0 ^{\circ}}{45} )}

化简

- \frac{cos ( \frac{- 18 0 ^{\circ} + 9 x}{9} )}{sin ( \frac{- 18 0 ^{\circ} + 9 x}{9} )} + \frac{sin ( \frac{45 x + 144 0 ^{\circ}}{45} )}{cos ( \frac{45 x + 144 0 ^{\circ}}{45} )} : \frac{- cos ( \frac{- 18 0 ^{\circ} + 9 x}{9} ) cos ( \frac{45 x + 144 0 ^{\circ}}{45} ) + sin ( \frac{45 x + 144 0 ^{\circ}}{45} ) sin ( \frac{9 x - 18 0 ^{\circ}}{9} )}{sin ( \frac{9 x - 18 0 ^{\circ}}{9} ) cos ( \frac{45 x + 144 0 ^{\circ}}{45} )}

- \frac{cos ( \frac{- 18 0 ^{\circ} + 9 x}{9} )}{sin ( \frac{- 18 0 ^{\circ} + 9 x}{9} )} + \frac{sin ( \frac{45 x + 144 0 ^{\circ}}{45} )}{cos ( \frac{45 x + 144 0 ^{\circ}}{45} )}

sin (\frac{- 18 0 ^{\circ} + 9 x}{9}), cos (\frac{45 x + 144 0 ^{\circ}}{45})

的最小公倍数:

sin (\frac{9 x - 18 0 ^{\circ}}{9}) cos (\frac{45 x + 144 0 ^{\circ}}{45})

sin (\frac{- 18 0 ^{\circ} + 9 x}{9}), cos (\frac{45 x + 144 0 ^{\circ}}{45})

最小公倍数 (LCM)

计算出由出现在

sin (\frac{- 18 0 ^{\circ} + 9 x}{9})

或

cos (\frac{45 x + 144 0 ^{\circ}}{45})

中的因子组成的表达式

= sin (\frac{9 x - 18 0 ^{\circ}}{9}) cos (\frac{45 x + 144 0 ^{\circ}}{45})

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

sin (\frac{9 x - 18 0 ^{\circ}}{9}) cos (\frac{45 x + 144 0 ^{\circ}}{45})

对于

\frac{cos ( \frac{- 18 0 ^{\circ} + 9 x}{9} )}{sin ( \frac{- 18 0 ^{\circ} + 9 x}{9} )} :

将分母和分子乘以

cos (\frac{45 x + 144 0 ^{\circ}}{45})

\frac{cos ( \frac{- 18 0 ^{\circ} + 9 x}{9} )}{sin ( \frac{- 18 0 ^{\circ} + 9 x}{9} )} = \frac{cos ( \frac{- 18 0 ^{\circ} + 9 x}{9} ) cos ( \frac{45 x + 144 0 ^{\circ}}{45} )}{sin ( \frac{- 18 0 ^{\circ} + 9 x}{9} ) cos ( \frac{45 x + 144 0 ^{\circ}}{45} )}

对于

\frac{sin ( \frac{45 x + 144 0 ^{\circ}}{45} )}{cos ( \frac{45 x + 144 0 ^{\circ}}{45} )} :

将分母和分子乘以

sin (\frac{9 x - 18 0 ^{\circ}}{9})

\frac{sin ( \frac{45 x + 144 0 ^{\circ}}{45} )}{cos ( \frac{45 x + 144 0 ^{\circ}}{45} )} = \frac{sin ( \frac{45 x + 144 0 ^{\circ}}{45} ) sin ( \frac{9 x - 18 0 ^{\circ}}{9} )}{cos ( \frac{45 x + 144 0 ^{\circ}}{45} ) sin ( \frac{9 x - 18 0 ^{\circ}}{9} )}

= - \frac{cos ( \frac{- 18 0 ^{\circ} + 9 x}{9} ) cos ( \frac{45 x + 144 0 ^{\circ}}{45} )}{sin ( \frac{- 18 0 ^{\circ} + 9 x}{9} ) cos ( \frac{45 x + 144 0 ^{\circ}}{45} )} + \frac{sin ( \frac{45 x + 144 0 ^{\circ}}{45} ) sin ( \frac{9 x - 18 0 ^{\circ}}{9} )}{cos ( \frac{45 x + 144 0 ^{\circ}}{45} ) sin ( \frac{9 x - 18 0 ^{\circ}}{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{- cos ( \frac{- 18 0 ^{\circ} + 9 x}{9} ) cos ( \frac{45 x + 144 0 ^{\circ}}{45} ) + sin ( \frac{45 x + 144 0 ^{\circ}}{45} ) sin ( \frac{9 x - 18 0 ^{\circ}}{9} )}{sin ( \frac{9 x - 18 0 ^{\circ}}{9} ) cos ( \frac{45 x + 144 0 ^{\circ}}{45} )}

= \frac{- cos ( \frac{- 18 0 ^{\circ} + 9 x}{9} ) cos ( \frac{45 x + 144 0 ^{\circ}}{45} ) + sin ( \frac{45 x + 144 0 ^{\circ}}{45} ) sin ( \frac{9 x - 18 0 ^{\circ}}{9} )}{sin ( \frac{9 x - 18 0 ^{\circ}}{9} ) cos ( \frac{45 x + 144 0 ^{\circ}}{45} )}

\frac{- cos ( \frac{- 18 0 ^{\circ} + 9 x}{9} ) cos ( \frac{45 x + 144 0 ^{\circ}}{45} ) + sin ( \frac{- 18 0 ^{\circ} + 9 x}{9} ) sin ( \frac{45 x + 144 0 ^{\circ}}{45} )}{cos ( \frac{45 x + 144 0 ^{\circ}}{45} ) sin ( \frac{- 18 0 ^{\circ} + 9 x}{9} )} = 0

\frac{f ( x )}{g ( x )} = 0 \Rightarrow f (x) = 0

- cos (\frac{- 18 0 ^{\circ} + 9 x}{9}) cos (\frac{45 x + 144 0 ^{\circ}}{45}) + sin (\frac{- 18 0 ^{\circ} + 9 x}{9}) sin (\frac{45 x + 144 0 ^{\circ}}{45}) = 0

使用三角恒等式改写

- cos (\frac{- 18 0 ^{\circ} + 9 x}{9}) cos (\frac{45 x + 144 0 ^{\circ}}{45}) + sin (\frac{- 18 0 ^{\circ} + 9 x}{9}) sin (\frac{45 x + 144 0 ^{\circ}}{45})

使用角和恒等式:

cos (s) cos (t) - sin (s) sin (t) = cos (s + t)

- cos (s) cos (t) + sin (s) sin (t) = - cos (s + t)

= - cos (\frac{- 18 0 ^{\circ} + 9 x}{9} + \frac{45 x + 144 0 ^{\circ}}{45})

- cos (\frac{- 18 0 ^{\circ} + 9 x}{9} + \frac{45 x + 144 0 ^{\circ}}{45}) = 0

两边除以

- 1

- cos (\frac{- 18 0 ^{\circ} + 9 x}{9} + \frac{45 x + 144 0 ^{\circ}}{45}) = 0

两边除以

- 1

\frac{- cos ( \frac{- 18 0 ^{\circ} + 9 x}{9} + \frac{45 x + 144 0 ^{\circ}}{45} )}{- 1} = \frac{0}{- 1}

化简

cos (\frac{- 18 0 ^{\circ} + 9 x}{9} + \frac{45 x + 144 0 ^{\circ}}{45}) = 0

cos (\frac{- 18 0 ^{\circ} + 9 x}{9} + \frac{45 x + 144 0 ^{\circ}}{45}) = 0

cos (\frac{- 18 0 ^{\circ} + 9 x}{9} + \frac{45 x + 144 0 ^{\circ}}{45}) = 0

的通解

cos (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} cos (x) 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{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} cos (x) - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2}

\frac{- 18 0 ^{\circ} + 9 x}{9} + \frac{45 x + 144 0 ^{\circ}}{45} = 9 0^{\circ} + 36 0^{\circ} n, \frac{- 18 0 ^{\circ} + 9 x}{9} + \frac{45 x + 144 0 ^{\circ}}{45} = 27 0^{\circ} + 36 0^{\circ} n

\frac{- 18 0 ^{\circ} + 9 x}{9} + \frac{45 x + 144 0 ^{\circ}}{45} = 9 0^{\circ} + 36 0^{\circ} n, \frac{- 18 0 ^{\circ} + 9 x}{9} + \frac{45 x + 144 0 ^{\circ}}{45} = 27 0^{\circ} + 36 0^{\circ} n

解

\frac{- 18 0 ^{\circ} + 9 x}{9} + \frac{45 x + 144 0 ^{\circ}}{45} = 9 0^{\circ} + 36 0^{\circ} n : x = 3 9^{\circ} + 18 0^{\circ} n

\frac{- 18 0 ^{\circ} + 9 x}{9} + \frac{45 x + 144 0 ^{\circ}}{45} = 9 0^{\circ} + 36 0^{\circ} n

乘以最小公倍数

\frac{- 18 0 ^{\circ} + 9 x}{9} + \frac{45 x + 144 0 ^{\circ}}{45} = 9 0^{\circ} + 36 0^{\circ} n

找到

9, 45, 2

的最小公倍数:

90

9, 45, 2

最小公倍数 (LCM)

9

质因数分解:

3 \cdot 3

9

9

除以

39 = 3 \cdot 3

= 3 \cdot 3

45

质因数分解:

3 \cdot 3 \cdot 5

45

45

除以

345 = 15 \cdot 3

= 3 \cdot 15

15

除以

315 = 5 \cdot 3

= 3 \cdot 3 \cdot 5

3, 5

都是质数，因此无法进一步因数分解

= 3 \cdot 3 \cdot 5

2

质因数分解:

2

2

2

是质数，因此无法因数分解

= 2

计算出由至少在以下一个数字中出现的因数组成的数字:

9, 45, 2

= 3 \cdot 3 \cdot 5 \cdot 2

数字相乘:

3 \cdot 3 \cdot 5 \cdot 2 = 90

= 90

乘以最小公倍数=

90

\frac{- 18 0 ^{\circ} + 9 x}{9} \cdot 90 + \frac{45 x + 144 0 ^{\circ}}{45} \cdot 90 = 9 0^{\circ} \cdot 90 + 36 0^{\circ} n \cdot 90

化简

\frac{- 18 0 ^{\circ} + 9 x}{9} \cdot 90 + \frac{45 x + 144 0 ^{\circ}}{45} \cdot 90 = 9 0^{\circ} \cdot 90 + 36 0^{\circ} n \cdot 90

化简

\frac{- 18 0 ^{\circ} + 9 x}{9} \cdot 90 : 10 (9 x - 18 0^{\circ})

\frac{- 18 0 ^{\circ} + 9 x}{9} \cdot 90

分式相乘:

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

= \frac{( - 18 0 ^{\circ} + 9 x ) \cdot 90}{9}

数字相除:

\frac{90}{9} = 10

= 10 (9 x - 18 0^{\circ})

化简

\frac{45 x + 144 0 ^{\circ}}{45} \cdot 90 : 2 (45 x + 144 0^{\circ})

\frac{45 x + 144 0 ^{\circ}}{45} \cdot 90

分式相乘:

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

= \frac{( 45 x + 144 0 ^{\circ} ) \cdot 90}{45}

数字相除:

\frac{90}{45} = 2

= 2 (45 x + 144 0^{\circ})

化简

9 0^{\circ} \cdot 90 : 810 0^{\circ}

9 0^{\circ} \cdot 90

分式相乘:

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

= 810 0^{\circ}

数字相除:

\frac{90}{2} = 45

= 810 0^{\circ}

化简

36 0^{\circ} n \cdot 90 : 3240 0^{\circ} n

36 0^{\circ} n \cdot 90

数字相乘:

2 \cdot 90 = 180

= 3240 0^{\circ} n

10 (9 x - 18 0^{\circ}) + 2 (45 x + 144 0^{\circ}) = 810 0^{\circ} + 3240 0^{\circ} n

10 (9 x - 18 0^{\circ}) + 2 (45 x + 144 0^{\circ}) = 810 0^{\circ} + 3240 0^{\circ} n

10 (9 x - 18 0^{\circ}) + 2 (45 x + 144 0^{\circ}) = 810 0^{\circ} + 3240 0^{\circ} n

展开

10 (9 x - 18 0^{\circ}) + 2 (45 x + 144 0^{\circ}) : 180 x + 108 0^{\circ}

10 (9 x - 18 0^{\circ}) + 2 (45 x + 144 0^{\circ})

乘开

10 (9 x - 18 0^{\circ}) : 90 x - 180 0^{\circ}

10 (9 x - 18 0^{\circ})

使用分配律:

a (b - c) = ab - a c

a = 10, b = 9 x, c = 18 0^{\circ}

= 10 \cdot 9 x - 180 0^{\circ}

数字相乘:

10 \cdot 9 = 90

= 90 x - 180 0^{\circ}

= 90 x - 180 0^{\circ} + 2 (45 x + 144 0^{\circ})

乘开

2 (45 x + 144 0^{\circ}) : 90 x + 288 0^{\circ}

2 (45 x + 144 0^{\circ})

使用分配律:

a (b + c) = ab + a c

a = 2, b = 45 x, c = 144 0^{\circ}

= 2 \cdot 45 x + 2 \cdot 144 0^{\circ}

化简

2 \cdot 45 x + 2 \cdot 144 0^{\circ} : 90 x + 288 0^{\circ}

2 \cdot 45 x + 2 \cdot 144 0^{\circ}

数字相乘:

2 \cdot 45 = 90

= 90 x + 2 \cdot 144 0^{\circ}

数字相乘:

2 \cdot 8 = 16

= 90 x + 288 0^{\circ}

= 90 x + 288 0^{\circ}

= 90 x - 180 0^{\circ} + 90 x + 288 0^{\circ}

化简

90 x - 180 0^{\circ} + 90 x + 288 0^{\circ} : 180 x + 108 0^{\circ}

90 x - 180 0^{\circ} + 90 x + 288 0^{\circ}

对同类项分组

= 90 x + 90 x - 180 0^{\circ} + 288 0^{\circ}

同类项相加:

90 x + 90 x = 180 x

= 180 x - 180 0^{\circ} + 288 0^{\circ}

同类项相加:

- 180 0^{\circ} + 288 0^{\circ} = 108 0^{\circ}

= 180 x + 108 0^{\circ}

= 180 x + 108 0^{\circ}

180 x + 108 0^{\circ} = 810 0^{\circ} + 3240 0^{\circ} n

将

108 0^{\circ}

到右边

180 x + 108 0^{\circ} = 810 0^{\circ} + 3240 0^{\circ} n

两边减去

108 0^{\circ}

180 x + 108 0^{\circ} - 108 0^{\circ} = 810 0^{\circ} + 3240 0^{\circ} n - 108 0^{\circ}

化简

180 x = 702 0^{\circ} + 3240 0^{\circ} n

180 x = 702 0^{\circ} + 3240 0^{\circ} n

两边除以

180

180 x = 702 0^{\circ} + 3240 0^{\circ} n

两边除以

180

\frac{180 x}{180} = 3 9^{\circ} + \frac{3240 0 ^{\circ} n}{180}

化简

\frac{180 x}{180} = 3 9^{\circ} + \frac{3240 0 ^{\circ} n}{180}

化简

\frac{180 x}{180} : x

\frac{180 x}{180}

数字相除:

\frac{180}{180} = 1

= x

化简

3 9^{\circ} + \frac{3240 0 ^{\circ} n}{180} : 3 9^{\circ} + 18 0^{\circ} n

3 9^{\circ} + \frac{3240 0 ^{\circ} n}{180}

消掉

3 9^{\circ} : 3 9^{\circ}

3 9^{\circ}

约分:

3

= 3 9^{\circ}

= 3 9^{\circ} + \frac{3240 0 ^{\circ} n}{180}

数字相除:

\frac{180}{180} = 1

= 3 9^{\circ} + 18 0^{\circ} n

x = 3 9^{\circ} + 18 0^{\circ} n

x = 3 9^{\circ} + 18 0^{\circ} n

x = 3 9^{\circ} + 18 0^{\circ} n

解

\frac{- 18 0 ^{\circ} + 9 x}{9} + \frac{45 x + 144 0 ^{\circ}}{45} = 27 0^{\circ} + 36 0^{\circ} n : x = 12 9^{\circ} + 18 0^{\circ} n

\frac{- 18 0 ^{\circ} + 9 x}{9} + \frac{45 x + 144 0 ^{\circ}}{45} = 27 0^{\circ} + 36 0^{\circ} n

乘以最小公倍数

\frac{- 18 0 ^{\circ} + 9 x}{9} + \frac{45 x + 144 0 ^{\circ}}{45} = 27 0^{\circ} + 36 0^{\circ} n

找到

9, 45, 2

的最小公倍数:

90

9, 45, 2

最小公倍数 (LCM)

9

质因数分解:

3 \cdot 3

9

9

除以

39 = 3 \cdot 3

= 3 \cdot 3

45

质因数分解:

3 \cdot 3 \cdot 5

45

45

除以

345 = 15 \cdot 3

= 3 \cdot 15

15

除以

315 = 5 \cdot 3

= 3 \cdot 3 \cdot 5

3, 5

都是质数，因此无法进一步因数分解

= 3 \cdot 3 \cdot 5

2

质因数分解:

2

2

2

是质数，因此无法因数分解

= 2

计算出由至少在以下一个数字中出现的因数组成的数字:

9, 45, 2

= 3 \cdot 3 \cdot 5 \cdot 2

数字相乘:

3 \cdot 3 \cdot 5 \cdot 2 = 90

= 90

乘以最小公倍数=

90

\frac{- 18 0 ^{\circ} + 9 x}{9} \cdot 90 + \frac{45 x + 144 0 ^{\circ}}{45} \cdot 90 = 27 0^{\circ} \cdot 90 + 36 0^{\circ} n \cdot 90

化简

\frac{- 18 0 ^{\circ} + 9 x}{9} \cdot 90 + \frac{45 x + 144 0 ^{\circ}}{45} \cdot 90 = 27 0^{\circ} \cdot 90 + 36 0^{\circ} n \cdot 90

化简

\frac{- 18 0 ^{\circ} + 9 x}{9} \cdot 90 : 10 (9 x - 18 0^{\circ})

\frac{- 18 0 ^{\circ} + 9 x}{9} \cdot 90

分式相乘:

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

= \frac{( - 18 0 ^{\circ} + 9 x ) \cdot 90}{9}

数字相除:

\frac{90}{9} = 10

= 10 (9 x - 18 0^{\circ})

化简

\frac{45 x + 144 0 ^{\circ}}{45} \cdot 90 : 2 (45 x + 144 0^{\circ})

\frac{45 x + 144 0 ^{\circ}}{45} \cdot 90

分式相乘:

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

= \frac{( 45 x + 144 0 ^{\circ} ) \cdot 90}{45}

数字相除:

\frac{90}{45} = 2

= 2 (45 x + 144 0^{\circ})

化简

27 0^{\circ} \cdot 90 : 2430 0^{\circ}

27 0^{\circ} \cdot 90

分式相乘:

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

= 2430 0^{\circ}

数字相乘:

3 \cdot 90 = 270

= 2430 0^{\circ}

数字相除:

\frac{270}{2} = 135

= 2430 0^{\circ}

化简

36 0^{\circ} n \cdot 90 : 3240 0^{\circ} n

36 0^{\circ} n \cdot 90

数字相乘:

2 \cdot 90 = 180

= 3240 0^{\circ} n

10 (9 x - 18 0^{\circ}) + 2 (45 x + 144 0^{\circ}) = 2430 0^{\circ} + 3240 0^{\circ} n

10 (9 x - 18 0^{\circ}) + 2 (45 x + 144 0^{\circ}) = 2430 0^{\circ} + 3240 0^{\circ} n

10 (9 x - 18 0^{\circ}) + 2 (45 x + 144 0^{\circ}) = 2430 0^{\circ} + 3240 0^{\circ} n

展开

10 (9 x - 18 0^{\circ}) + 2 (45 x + 144 0^{\circ}) : 180 x + 108 0^{\circ}

10 (9 x - 18 0^{\circ}) + 2 (45 x + 144 0^{\circ})

乘开

10 (9 x - 18 0^{\circ}) : 90 x - 180 0^{\circ}

10 (9 x - 18 0^{\circ})

使用分配律:

a (b - c) = ab - a c

a = 10, b = 9 x, c = 18 0^{\circ}

= 10 \cdot 9 x - 180 0^{\circ}

数字相乘:

10 \cdot 9 = 90

= 90 x - 180 0^{\circ}

= 90 x - 180 0^{\circ} + 2 (45 x + 144 0^{\circ})

乘开

2 (45 x + 144 0^{\circ}) : 90 x + 288 0^{\circ}

2 (45 x + 144 0^{\circ})

使用分配律:

a (b + c) = ab + a c

a = 2, b = 45 x, c = 144 0^{\circ}

= 2 \cdot 45 x + 2 \cdot 144 0^{\circ}

化简

2 \cdot 45 x + 2 \cdot 144 0^{\circ} : 90 x + 288 0^{\circ}

2 \cdot 45 x + 2 \cdot 144 0^{\circ}

数字相乘:

2 \cdot 45 = 90

= 90 x + 2 \cdot 144 0^{\circ}

数字相乘:

2 \cdot 8 = 16

= 90 x + 288 0^{\circ}

= 90 x + 288 0^{\circ}

= 90 x - 180 0^{\circ} + 90 x + 288 0^{\circ}

化简

90 x - 180 0^{\circ} + 90 x + 288 0^{\circ} : 180 x + 108 0^{\circ}

90 x - 180 0^{\circ} + 90 x + 288 0^{\circ}

对同类项分组

= 90 x + 90 x - 180 0^{\circ} + 288 0^{\circ}

同类项相加:

90 x + 90 x = 180 x

= 180 x - 180 0^{\circ} + 288 0^{\circ}

同类项相加:

- 180 0^{\circ} + 288 0^{\circ} = 108 0^{\circ}

= 180 x + 108 0^{\circ}

= 180 x + 108 0^{\circ}

180 x + 108 0^{\circ} = 2430 0^{\circ} + 3240 0^{\circ} n

将

108 0^{\circ}

到右边

180 x + 108 0^{\circ} = 2430 0^{\circ} + 3240 0^{\circ} n

两边减去

108 0^{\circ}

180 x + 108 0^{\circ} - 108 0^{\circ} = 2430 0^{\circ} + 3240 0^{\circ} n - 108 0^{\circ}

化简

180 x = 2322 0^{\circ} + 3240 0^{\circ} n

180 x = 2322 0^{\circ} + 3240 0^{\circ} n

两边除以

180

180 x = 2322 0^{\circ} + 3240 0^{\circ} n

两边除以

180

\frac{180 x}{180} = 12 9^{\circ} + \frac{3240 0 ^{\circ} n}{180}

化简

\frac{180 x}{180} = 12 9^{\circ} + \frac{3240 0 ^{\circ} n}{180}

化简

\frac{180 x}{180} : x

\frac{180 x}{180}

数字相除:

\frac{180}{180} = 1

= x

化简

12 9^{\circ} + \frac{3240 0 ^{\circ} n}{180} : 12 9^{\circ} + 18 0^{\circ} n

12 9^{\circ} + \frac{3240 0 ^{\circ} n}{180}

消掉

12 9^{\circ} : 12 9^{\circ}

12 9^{\circ}

约分:

3

= 12 9^{\circ}

= 12 9^{\circ} + \frac{3240 0 ^{\circ} n}{180}

数字相除:

\frac{180}{180} = 1

= 12 9^{\circ} + 18 0^{\circ} n

x = 12 9^{\circ} + 18 0^{\circ} n

x = 12 9^{\circ} + 18 0^{\circ} n

x = 12 9^{\circ} + 18 0^{\circ} n

x = 3 9^{\circ} + 18 0^{\circ} n, x = 12 9^{\circ} + 18 0^{\circ} n

作图

流行的例子

cosh (z) = - 1

0 = sin (2 θ)

6 sin (θ) + 1 = 0

17cos(x)+9=-cos(x)

17 cos (x) + 9 = - cos (x)

(2cos(θ)+1)(cos(θ)-2)=0

(2 cos (θ) + 1) (cos (θ) - 2) = 0