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受欢迎的三角函数 >

sin(x)=cos(2x+51)

解答

sin (x) = cos (2 x + 5 1^{\circ})

解答

x = \frac{2160 0 ^{\circ} n + 234 0 ^{\circ}}{180}, x = - \frac{846 0 ^{\circ} + 2160 0 ^{\circ} n}{60}

+1

弧度

x = \frac{\frac{13 π}{5}}{36} + \frac{120 π}{180} n, x = - \frac{\frac{47 π}{5}}{12} - \frac{120 π}{60} n

求解步骤

sin (x) = cos (2 x + 5 1^{\circ})

使用三角恒等式改写

sin (x) = cos (2 x + 5 1^{\circ})

利用以下特性:

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

sin (x) = sin (9 0^{\circ} - (2 x + 5 1^{\circ}))

sin (x) = sin (9 0^{\circ} - (2 x + 5 1^{\circ}))

使用反三角函数性质

sin (x) = sin (9 0^{\circ} - (2 x + 5 1^{\circ}))

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

x = 9 0^{\circ} - (2 x + 5 1^{\circ}) + 36 0^{\circ} n, x = 18 0^{\circ} - (9 0^{\circ} - (2 x + 5 1^{\circ})) + 36 0^{\circ} n

x = 9 0^{\circ} - (2 x + 5 1^{\circ}) + 36 0^{\circ} n, x = 18 0^{\circ} - (9 0^{\circ} - (2 x + 5 1^{\circ})) + 36 0^{\circ} n

x = 9 0^{\circ} - (2 x + 5 1^{\circ}) + 36 0^{\circ} n : x = \frac{2160 0 ^{\circ} n + 234 0 ^{\circ}}{180}

x = 9 0^{\circ} - (2 x + 5 1^{\circ}) + 36 0^{\circ} n

展开

9 0^{\circ} - (2 x + 5 1^{\circ}) + 36 0^{\circ} n : - 2 x + 36 0^{\circ} n + 3 9^{\circ}

9 0^{\circ} - (2 x + 5 1^{\circ}) + 36 0^{\circ} n

- (2 x + 5 1^{\circ}) : - 2 x - 5 1^{\circ}

- (2 x + 5 1^{\circ})

打开括号

= - (2 x) - (5 1^{\circ})

使用加减运算法则

+ (- a) = - a

= - 2 x - 5 1^{\circ}

= 9 0^{\circ} - 2 x - 5 1^{\circ} + 36 0^{\circ} n

化简

9 0^{\circ} - 2 x - 5 1^{\circ} + 36 0^{\circ} n : - 2 x + 36 0^{\circ} n + 3 9^{\circ}

9 0^{\circ} - 2 x - 5 1^{\circ} + 36 0^{\circ} n

对同类项分组

= - 2 x + 36 0^{\circ} n + 9 0^{\circ} - 5 1^{\circ}

2, 60

的最小公倍数:

60

2, 60

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

60

质因数分解:

2 \cdot 2 \cdot 3 \cdot 5

60

60

除以

260 = 30 \cdot 2

= 2 \cdot 30

30

除以

230 = 15 \cdot 2

= 2 \cdot 2 \cdot 15

15

除以

315 = 5 \cdot 3

= 2 \cdot 2 \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 5

将每个因子乘以它在

2

或

60

中出现的最多次数

= 2 \cdot 2 \cdot 3 \cdot 5

数字相乘:

2 \cdot 2 \cdot 3 \cdot 5 = 60

= 60

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

60

对于

9 0^{\circ} :

将分母和分子乘以

30

9 0^{\circ} = \frac{18 0 ^{\circ} 30}{2 \cdot 30} = 9 0^{\circ}

= 9 0^{\circ} - 5 1^{\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} 30 - 306 0 ^{\circ}}{60}

同类项相加:

540 0^{\circ} - 306 0^{\circ} = 234 0^{\circ}

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

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

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

将

2 x

para o lado esquerdo

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

两边加上

2 x

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

化简

3 x = 36 0^{\circ} n + 3 9^{\circ}

3 x = 36 0^{\circ} n + 3 9^{\circ}

两边除以

3

3 x = 36 0^{\circ} n + 3 9^{\circ}

两边除以

3

\frac{3 x}{3} = \frac{36 0 ^{\circ} n}{3} + \frac{3 9 ^{\circ}}{3}

化简

\frac{3 x}{3} = \frac{36 0 ^{\circ} n}{3} + \frac{3 9 ^{\circ}}{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{3 9 ^{\circ}}{3} : \frac{2160 0 ^{\circ} n + 234 0 ^{\circ}}{180}

\frac{36 0 ^{\circ} n}{3} + \frac{3 9 ^{\circ}}{3}

使用法则

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

= \frac{36 0 ^{\circ} n + 3 9 ^{\circ}}{3}

化简

36 0^{\circ} n + 3 9^{\circ} : \frac{2160 0 ^{\circ} n + 234 0 ^{\circ}}{60}

36 0^{\circ} n + 3 9^{\circ}

将项转换为分式:

36 0^{\circ} n = \frac{36 0 ^{\circ} n 60}{60}

= \frac{36 0 ^{\circ} n \cdot 60}{60} + 3 9^{\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{36 0 ^{\circ} n \cdot 60 + 234 0 ^{\circ}}{60}

数字相乘:

2 \cdot 60 = 120

= \frac{2160 0 ^{\circ} n + 234 0 ^{\circ}}{60}

= \frac{\frac{2160 0 ^{\circ} n + 234 0 ^{\circ}}{60}}{3}

使用分式法则:

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

= \frac{2160 0 ^{\circ} n + 234 0 ^{\circ}}{60 \cdot 3}

数字相乘:

60 \cdot 3 = 180

= \frac{2160 0 ^{\circ} n + 234 0 ^{\circ}}{180}

x = \frac{2160 0 ^{\circ} n + 234 0 ^{\circ}}{180}

x = \frac{2160 0 ^{\circ} n + 234 0 ^{\circ}}{180}

x = \frac{2160 0 ^{\circ} n + 234 0 ^{\circ}}{180}

x = 18 0^{\circ} - (9 0^{\circ} - (2 x + 5 1^{\circ})) + 36 0^{\circ} n : x = - \frac{846 0 ^{\circ} + 2160 0 ^{\circ} n}{60}

x = 18 0^{\circ} - (9 0^{\circ} - (2 x + 5 1^{\circ})) + 36 0^{\circ} n

展开

18 0^{\circ} - (9 0^{\circ} - (2 x + 5 1^{\circ})) + 36 0^{\circ} n : 18 0^{\circ} + 2 x - 3 9^{\circ} + 36 0^{\circ} n

18 0^{\circ} - (9 0^{\circ} - (2 x + 5 1^{\circ})) + 36 0^{\circ} n

乘开

9 0^{\circ} - (2 x + 5 1^{\circ}) : - 2 x + 3 9^{\circ}

9 0^{\circ} - (2 x + 5 1^{\circ})

- (2 x + 5 1^{\circ}) : - 2 x - 5 1^{\circ}

- (2 x + 5 1^{\circ})

打开括号

= - (2 x) - (5 1^{\circ})

使用加减运算法则

+ (- a) = - a

= - 2 x - 5 1^{\circ}

= 9 0^{\circ} - 2 x - 5 1^{\circ}

化简

9 0^{\circ} - 2 x - 5 1^{\circ} : - 2 x + 3 9^{\circ}

9 0^{\circ} - 2 x - 5 1^{\circ}

对同类项分组

= - 2 x + 9 0^{\circ} - 5 1^{\circ}

2, 60

的最小公倍数:

60

2, 60

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

60

质因数分解:

2 \cdot 2 \cdot 3 \cdot 5

60

60

除以

260 = 30 \cdot 2

= 2 \cdot 30

30

除以

230 = 15 \cdot 2

= 2 \cdot 2 \cdot 15

15

除以

315 = 5 \cdot 3

= 2 \cdot 2 \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 5

将每个因子乘以它在

2

或

60

中出现的最多次数

= 2 \cdot 2 \cdot 3 \cdot 5

数字相乘:

2 \cdot 2 \cdot 3 \cdot 5 = 60

= 60

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

60

对于

9 0^{\circ} :

将分母和分子乘以

30

9 0^{\circ} = \frac{18 0 ^{\circ} 30}{2 \cdot 30} = 9 0^{\circ}

= 9 0^{\circ} - 5 1^{\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} 30 - 306 0 ^{\circ}}{60}

同类项相加:

540 0^{\circ} - 306 0^{\circ} = 234 0^{\circ}

= - 2 x + 3 9^{\circ}

= - 2 x + 3 9^{\circ}

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

- (- 2 x + 3 9^{\circ}) : 2 x - 3 9^{\circ}

- (- 2 x + 3 9^{\circ})

打开括号

= - (- 2 x) - (3 9^{\circ})

使用加减运算法则

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

= 2 x - 3 9^{\circ}

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

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

将

2 x

para o lado esquerdo

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

两边减去

2 x

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

化简

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

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

两边除以

- 1

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

两边除以

- 1

\frac{- x}{- 1} = \frac{18 0 ^{\circ}}{- 1} - \frac{3 9 ^{\circ}}{- 1} + \frac{36 0 ^{\circ} n}{- 1}

化简

\frac{- x}{- 1} = \frac{18 0 ^{\circ}}{- 1} - \frac{3 9 ^{\circ}}{- 1} + \frac{36 0 ^{\circ} n}{- 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{3 9 ^{\circ}}{- 1} + \frac{36 0 ^{\circ} n}{- 1} : - \frac{846 0 ^{\circ} + 2160 0 ^{\circ} n}{60}

\frac{18 0 ^{\circ}}{- 1} - \frac{3 9 ^{\circ}}{- 1} + \frac{36 0 ^{\circ} n}{- 1}

使用法则

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

= \frac{18 0 ^{\circ} - 3 9 ^{\circ} + 36 0 ^{\circ} n}{- 1}

使用分式法则:

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

= - \frac{18 0 ^{\circ} - 3 9 ^{\circ} + 36 0 ^{\circ} n}{1}

化简

18 0^{\circ} - 3 9^{\circ} + 36 0^{\circ} n : \frac{846 0 ^{\circ} + 2160 0 ^{\circ} n}{60}

18 0^{\circ} - 3 9^{\circ} + 36 0^{\circ} n

将项转换为分式:

18 0^{\circ} = 18 0^{\circ}, 36 0^{\circ} n = \frac{36 0 ^{\circ} n 60}{60}

= 18 0^{\circ} - 3 9^{\circ} + \frac{36 0 ^{\circ} n \cdot 60}{60}

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} 60 - 234 0 ^{\circ} + 36 0 ^{\circ} n \cdot 60}{60}

18 0^{\circ} 60 - 234 0^{\circ} + 36 0^{\circ} n \cdot 60 = 846 0^{\circ} + 2160 0^{\circ} n

18 0^{\circ} 60 - 234 0^{\circ} + 36 0^{\circ} n \cdot 60

同类项相加:

1080 0^{\circ} - 234 0^{\circ} = 846 0^{\circ}

= 846 0^{\circ} + 2 \cdot 1080 0^{\circ} n

数字相乘:

2 \cdot 60 = 120

= 846 0^{\circ} + 2160 0^{\circ} n

= \frac{846 0 ^{\circ} + 2160 0 ^{\circ} n}{60}

= - \frac{\frac{846 0 ^{\circ} + 2160 0 ^{\circ} n}{60}}{1}

使用分式法则:

\frac{a}{1} = a

= - \frac{846 0 ^{\circ} + 2160 0 ^{\circ} n}{60}

x = - \frac{846 0 ^{\circ} + 2160 0 ^{\circ} n}{60}

x = - \frac{846 0 ^{\circ} + 2160 0 ^{\circ} n}{60}

x = - \frac{846 0 ^{\circ} + 2160 0 ^{\circ} n}{60}

x = \frac{2160 0 ^{\circ} n + 234 0 ^{\circ}}{180}, x = - \frac{846 0 ^{\circ} + 2160 0 ^{\circ} n}{60}

x = \frac{2160 0 ^{\circ} n + 234 0 ^{\circ}}{180}, x = - \frac{846 0 ^{\circ} + 2160 0 ^{\circ} n}{60}

作图

流行的例子

sin (x) = \frac{π}{4}

cos (x) = 45.7

tan(5x)*cot(x+40)=1

tan (5 x) \cdot cot (x + 4 0^{\circ}) = 1

sin (θ) = 0.7043

3 cosh (2 x) = 5