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受欢迎的三角函数 >

sin(2x+4)=cos(46)

解答

sin (2 x + 4) = cos (4 6^{\circ})

解答

x = \frac{1620 0 ^{\circ} n + 198 0 ^{\circ} - 180}{90}, x = \frac{306 0 ^{\circ} + 810 0 ^{\circ} n - 90}{45}

+1

弧度

x = \frac{\frac{11 π}{5}}{18} - 2 + \frac{90 π}{90} n, x = - 2 + \frac{\frac{17 π}{5}}{9} + \frac{45 π}{45} n

求解步骤

sin (2 x + 4) = cos (4 6^{\circ})

使用三角恒等式改写

cos (4 6^{\circ})

利用以下特性:

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

sin (9 0^{\circ} - 4 6^{\circ})

sin (2 x + 4) = sin (9 0^{\circ} - 4 6^{\circ})

使用反三角函数性质

sin (2 x + 4) = sin (9 0^{\circ} - 4 6^{\circ})

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

2 x + 4 = 9 0^{\circ} - 4 6^{\circ} + 36 0^{\circ} n, 2 x + 4 = 18 0^{\circ} - (9 0^{\circ} - 4 6^{\circ}) + 36 0^{\circ} n

2 x + 4 = 9 0^{\circ} - 4 6^{\circ} + 36 0^{\circ} n, 2 x + 4 = 18 0^{\circ} - (9 0^{\circ} - 4 6^{\circ}) + 36 0^{\circ} n

2 x + 4 = 9 0^{\circ} - 4 6^{\circ} + 36 0^{\circ} n : x = \frac{1620 0 ^{\circ} n + 198 0 ^{\circ} - 180}{90}

2 x + 4 = 9 0^{\circ} - 4 6^{\circ} + 36 0^{\circ} n

将

4

到右边

2 x + 4 = 9 0^{\circ} - 4 6^{\circ} + 36 0^{\circ} n

两边减去

4

2 x + 4 - 4 = 9 0^{\circ} - 4 6^{\circ} + 36 0^{\circ} n - 4

化简

2 x + 4 - 4 = 9 0^{\circ} - 4 6^{\circ} + 36 0^{\circ} n - 4

化简

2 x + 4 - 4 : 2 x

2 x + 4 - 4

同类项相加:

4 - 4 = 0

= 2 x

化简

9 0^{\circ} - 4 6^{\circ} + 36 0^{\circ} n - 4 : 36 0^{\circ} n + 4 4^{\circ} - 4

9 0^{\circ} - 4 6^{\circ} + 36 0^{\circ} n - 4

合并分式

9 0^{\circ} - 4 6^{\circ} : 4 4^{\circ}

9 0^{\circ} - 4 6^{\circ}

2, 90

的最小公倍数:

90

2, 90

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

90

质因数分解:

2 \cdot 3 \cdot 3 \cdot 5

90

90

除以

290 = 45 \cdot 2

= 2 \cdot 45

45

除以

345 = 15 \cdot 3

= 2 \cdot 3 \cdot 15

15

除以

315 = 5 \cdot 3

= 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 3 \cdot 3 \cdot 5

将每个因子乘以它在

2

或

90

中出现的最多次数

= 2 \cdot 3 \cdot 3 \cdot 5

数字相乘:

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

= 90

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

90

对于

9 0^{\circ} :

将分母和分子乘以

45

9 0^{\circ} = \frac{18 0 ^{\circ} 45}{2 \cdot 45} = 9 0^{\circ}

= 9 0^{\circ} - 4 6^{\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} 45 - 414 0 ^{\circ}}{90}

同类项相加:

810 0^{\circ} - 414 0^{\circ} = 396 0^{\circ}

= 4 4^{\circ}

约分:

2

= 4 4^{\circ}

= 36 0^{\circ} n + 4 4^{\circ} - 4

2 x = 36 0^{\circ} n + 4 4^{\circ} - 4

2 x = 36 0^{\circ} n + 4 4^{\circ} - 4

2 x = 36 0^{\circ} n + 4 4^{\circ} - 4

两边除以

2

2 x = 36 0^{\circ} n + 4 4^{\circ} - 4

两边除以

2

\frac{2 x}{2} = \frac{36 0 ^{\circ} n}{2} + \frac{4 4 ^{\circ}}{2} - \frac{4}{2}

化简

\frac{2 x}{2} = \frac{36 0 ^{\circ} n}{2} + \frac{4 4 ^{\circ}}{2} - \frac{4}{2}

化简

\frac{2 x}{2} : x

\frac{2 x}{2}

数字相除:

\frac{2}{2} = 1

= x

化简

\frac{36 0 ^{\circ} n}{2} + \frac{4 4 ^{\circ}}{2} - \frac{4}{2} : \frac{1620 0 ^{\circ} n + 198 0 ^{\circ} - 180}{90}

\frac{36 0 ^{\circ} n}{2} + \frac{4 4 ^{\circ}}{2} - \frac{4}{2}

使用法则

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

= \frac{36 0 ^{\circ} n + 4 4 ^{\circ} - 4}{2}

化简

36 0^{\circ} n + 4 4^{\circ} - 4 : \frac{1620 0 ^{\circ} n + 198 0 ^{\circ} - 180}{45}

36 0^{\circ} n + 4 4^{\circ} - 4

将项转换为分式:

36 0^{\circ} n = \frac{36 0 ^{\circ} n 45}{45}, 4 = \frac{4 \cdot 45}{45}

= \frac{36 0 ^{\circ} n \cdot 45}{45} + 4 4^{\circ} - \frac{4 \cdot 45}{45}

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 45 + 198 0 ^{\circ} - 4 \cdot 45}{45}

36 0^{\circ} n \cdot 45 + 198 0^{\circ} - 4 \cdot 45 = 1620 0^{\circ} n + 198 0^{\circ} - 180

36 0^{\circ} n \cdot 45 + 198 0^{\circ} - 4 \cdot 45

数字相乘:

2 \cdot 45 = 90

= 1620 0^{\circ} n + 198 0^{\circ} - 4 \cdot 45

数字相乘:

4 \cdot 45 = 180

= 1620 0^{\circ} n + 198 0^{\circ} - 180

= \frac{1620 0 ^{\circ} n + 198 0 ^{\circ} - 180}{45}

= \frac{\frac{1620 0 ^{\circ} n + 198 0 ^{\circ} - 180}{45}}{2}

使用分式法则:

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

= \frac{1620 0 ^{\circ} n + 198 0 ^{\circ} - 180}{45 \cdot 2}

数字相乘:

45 \cdot 2 = 90

= \frac{1620 0 ^{\circ} n + 198 0 ^{\circ} - 180}{90}

x = \frac{1620 0 ^{\circ} n + 198 0 ^{\circ} - 180}{90}

x = \frac{1620 0 ^{\circ} n + 198 0 ^{\circ} - 180}{90}

x = \frac{1620 0 ^{\circ} n + 198 0 ^{\circ} - 180}{90}

2 x + 4 = 18 0^{\circ} - (9 0^{\circ} - 4 6^{\circ}) + 36 0^{\circ} n : x = \frac{306 0 ^{\circ} + 810 0 ^{\circ} n - 90}{45}

2 x + 4 = 18 0^{\circ} - (9 0^{\circ} - 4 6^{\circ}) + 36 0^{\circ} n

将

4

到右边

2 x + 4 = 18 0^{\circ} - (9 0^{\circ} - 4 6^{\circ}) + 36 0^{\circ} n

两边减去

4

2 x + 4 - 4 = 18 0^{\circ} - (9 0^{\circ} - 4 6^{\circ}) + 36 0^{\circ} n - 4

化简

2 x + 4 - 4 = 18 0^{\circ} - (9 0^{\circ} - 4 6^{\circ}) + 36 0^{\circ} n - 4

化简

2 x + 4 - 4 : 2 x

2 x + 4 - 4

同类项相加:

4 - 4 = 0

= 2 x

化简

18 0^{\circ} - (9 0^{\circ} - 4 6^{\circ}) + 36 0^{\circ} n - 4 : 18 0^{\circ} - 4 4^{\circ} + 36 0^{\circ} n - 4

18 0^{\circ} - (9 0^{\circ} - 4 6^{\circ}) + 36 0^{\circ} n - 4

化简

9 0^{\circ} - 4 6^{\circ} : 4 4^{\circ}

9 0^{\circ} - 4 6^{\circ}

2, 90

的最小公倍数:

90

2, 90

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

90

质因数分解:

2 \cdot 3 \cdot 3 \cdot 5

90

90

除以

290 = 45 \cdot 2

= 2 \cdot 45

45

除以

345 = 15 \cdot 3

= 2 \cdot 3 \cdot 15

15

除以

315 = 5 \cdot 3

= 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 3 \cdot 3 \cdot 5

将每个因子乘以它在

2

或

90

中出现的最多次数

= 2 \cdot 3 \cdot 3 \cdot 5

数字相乘:

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

= 90

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

90

对于

9 0^{\circ} :

将分母和分子乘以

45

9 0^{\circ} = \frac{18 0 ^{\circ} 45}{2 \cdot 45} = 9 0^{\circ}

= 9 0^{\circ} - 4 6^{\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} 45 - 414 0 ^{\circ}}{90}

同类项相加:

810 0^{\circ} - 414 0^{\circ} = 396 0^{\circ}

= 4 4^{\circ}

约分:

2

= 4 4^{\circ}

= 18 0^{\circ} - 4 4^{\circ} + 36 0^{\circ} n - 4

2 x = 18 0^{\circ} - 4 4^{\circ} + 36 0^{\circ} n - 4

2 x = 18 0^{\circ} - 4 4^{\circ} + 36 0^{\circ} n - 4

2 x = 18 0^{\circ} - 4 4^{\circ} + 36 0^{\circ} n - 4

两边除以

2

2 x = 18 0^{\circ} - 4 4^{\circ} + 36 0^{\circ} n - 4

两边除以

2

\frac{2 x}{2} = 9 0^{\circ} - \frac{4 4 ^{\circ}}{2} + \frac{36 0 ^{\circ} n}{2} - \frac{4}{2}

化简

\frac{2 x}{2} = 9 0^{\circ} - \frac{4 4 ^{\circ}}{2} + \frac{36 0 ^{\circ} n}{2} - \frac{4}{2}

化简

\frac{2 x}{2} : x

\frac{2 x}{2}

数字相除:

\frac{2}{2} = 1

= x

化简

9 0^{\circ} - \frac{4 4 ^{\circ}}{2} + \frac{36 0 ^{\circ} n}{2} - \frac{4}{2} : \frac{306 0 ^{\circ} + 810 0 ^{\circ} n - 90}{45}

9 0^{\circ} - \frac{4 4 ^{\circ}}{2} + \frac{36 0 ^{\circ} n}{2} - \frac{4}{2}

对同类项分组

= 9 0^{\circ} - \frac{4}{2} + \frac{36 0 ^{\circ} n}{2} - \frac{4 4 ^{\circ}}{2}

使用法则

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

= \frac{18 0 ^{\circ} - 4 + 36 0 ^{\circ} n - 4 4 ^{\circ}}{2}

化简

18 0^{\circ} - 4 + 36 0^{\circ} n - 4 4^{\circ} : \frac{612 0 ^{\circ} + 1620 0 ^{\circ} n - 180}{45}

18 0^{\circ} - 4 + 36 0^{\circ} n - 4 4^{\circ}

将项转换为分式:

18 0^{\circ} = 18 0^{\circ}, 4 = \frac{4 \cdot 45}{45}, 36 0^{\circ} n = \frac{36 0 ^{\circ} n 45}{45}

= 18 0^{\circ} - \frac{4 \cdot 45}{45} + \frac{36 0 ^{\circ} n \cdot 45}{45} - 4 4^{\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} 45 - 4 \cdot 45 + 36 0 ^{\circ} n \cdot 45 - 198 0 ^{\circ}}{45}

18 0^{\circ} 45 - 4 \cdot 45 + 36 0^{\circ} n \cdot 45 - 198 0^{\circ} = 612 0^{\circ} + 1620 0^{\circ} n - 180

18 0^{\circ} 45 - 4 \cdot 45 + 36 0^{\circ} n \cdot 45 - 198 0^{\circ}

对同类项分组

= 810 0^{\circ} - 198 0^{\circ} + 2 \cdot 810 0^{\circ} n - 4 \cdot 45

同类项相加:

810 0^{\circ} - 198 0^{\circ} = 612 0^{\circ}

= 612 0^{\circ} + 2 \cdot 810 0^{\circ} n - 4 \cdot 45

数字相乘:

2 \cdot 45 = 90

= 612 0^{\circ} + 1620 0^{\circ} n - 4 \cdot 45

数字相乘:

4 \cdot 45 = 180

= 612 0^{\circ} + 1620 0^{\circ} n - 180

= \frac{612 0 ^{\circ} + 1620 0 ^{\circ} n - 180}{45}

= \frac{\frac{612 0 ^{\circ} + 1620 0 ^{\circ} n - 180}{45}}{2}

使用分式法则:

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

= \frac{612 0 ^{\circ} + 1620 0 ^{\circ} n - 180}{45 \cdot 2}

数字相乘:

45 \cdot 2 = 90

= \frac{612 0 ^{\circ} + 1620 0 ^{\circ} n - 180}{90}

分解

612 0^{\circ} + 1620 0^{\circ} n - 180 : 2 (306 0^{\circ} + 810 0^{\circ} n - 90)

612 0^{\circ} + 1620 0^{\circ} n - 180

改写为

= 2 \cdot 306 0^{\circ} + 2 \cdot 810 0^{\circ} n - 2 \cdot 90

因式分解出通项

2

= 2 (306 0^{\circ} + 810 0^{\circ} n - 90)

= \frac{2 ( 306 0 ^{\circ} + 810 0 ^{\circ} n - 90 )}{90}

约分:

2

= \frac{306 0 ^{\circ} + 810 0 ^{\circ} n - 90}{45}

x = \frac{306 0 ^{\circ} + 810 0 ^{\circ} n - 90}{45}

x = \frac{306 0 ^{\circ} + 810 0 ^{\circ} n - 90}{45}

x = \frac{306 0 ^{\circ} + 810 0 ^{\circ} n - 90}{45}

x = \frac{1620 0 ^{\circ} n + 198 0 ^{\circ} - 180}{90}, x = \frac{306 0 ^{\circ} + 810 0 ^{\circ} n - 90}{45}

作图

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