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受欢迎的三角函数 >

cos(45-x)= 1/2

解答

cos (4 5^{\circ} - x) = \frac{1}{2}

解答

x = - 36 0^{\circ} n - 1 5^{\circ}, x = - 36 0^{\circ} n - 25 5^{\circ}

+1

弧度

x = - \frac{π}{12} - 2 πn, x = - \frac{17 π}{12} - 2 πn

求解步骤

cos (4 5^{\circ} - x) = \frac{1}{2}

cos (4 5^{\circ} - x) = \frac{1}{2}

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}

4 5^{\circ} - x = 6 0^{\circ} + 36 0^{\circ} n, 4 5^{\circ} - x = 30 0^{\circ} + 36 0^{\circ} n

4 5^{\circ} - x = 6 0^{\circ} + 36 0^{\circ} n, 4 5^{\circ} - x = 30 0^{\circ} + 36 0^{\circ} n

解

4 5^{\circ} - x = 6 0^{\circ} + 36 0^{\circ} n : x = - 36 0^{\circ} n - 1 5^{\circ}

4 5^{\circ} - x = 6 0^{\circ} + 36 0^{\circ} n

将

4 5^{\circ}

到右边

4 5^{\circ} - x = 6 0^{\circ} + 36 0^{\circ} n

两边减去

4 5^{\circ}

4 5^{\circ} - x - 4 5^{\circ} = 6 0^{\circ} + 36 0^{\circ} n - 4 5^{\circ}

化简

4 5^{\circ} - x - 4 5^{\circ} = 6 0^{\circ} + 36 0^{\circ} n - 4 5^{\circ}

化简

4 5^{\circ} - x - 4 5^{\circ} : - x

4 5^{\circ} - x - 4 5^{\circ}

同类项相加:

4 5^{\circ} - 4 5^{\circ} = 0

= - x

化简

6 0^{\circ} + 36 0^{\circ} n - 4 5^{\circ} : 36 0^{\circ} n + 1 5^{\circ}

6 0^{\circ} + 36 0^{\circ} n - 4 5^{\circ}

对同类项分组

= 36 0^{\circ} n + 6 0^{\circ} - 4 5^{\circ}

3, 4

的最小公倍数:

12

3, 4

最小公倍数 (LCM)

3

质因数分解:

3

3

3

是质数，因此无法因数分解

= 3

4

质因数分解:

2 \cdot 2

4

4

除以

24 = 2 \cdot 2

= 2 \cdot 2

将每个因子乘以它在

3

或

4

中出现的最多次数

= 3 \cdot 2 \cdot 2

数字相乘:

3 \cdot 2 \cdot 2 = 12

= 12

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

12

对于

6 0^{\circ} :

将分母和分子乘以

4

6 0^{\circ} = \frac{18 0 ^{\circ} 4}{3 \cdot 4} = 6 0^{\circ}

对于

4 5^{\circ} :

将分母和分子乘以

3

4 5^{\circ} = \frac{18 0 ^{\circ} 3}{4 \cdot 3} = 4 5^{\circ}

= 6 0^{\circ} - 4 5^{\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} 4 - 18 0 ^{\circ} 3}{12}

同类项相加:

72 0^{\circ} - 54 0^{\circ} = 18 0^{\circ}

= 36 0^{\circ} n + 1 5^{\circ}

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

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

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

两边除以

- 1

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

两边除以

- 1

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

化简

\frac{- x}{- 1} = \frac{36 0 ^{\circ} n}{- 1} + \frac{1 5 ^{\circ}}{- 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{36 0 ^{\circ} n}{- 1} + \frac{1 5 ^{\circ}}{- 1} : - 36 0^{\circ} n - 1 5^{\circ}

\frac{36 0 ^{\circ} n}{- 1} + \frac{1 5 ^{\circ}}{- 1}

\frac{36 0 ^{\circ} n}{- 1} = - 36 0^{\circ} n

\frac{36 0 ^{\circ} n}{- 1}

使用分式法则:

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

= - \frac{36 0 ^{\circ} n}{1}

使用法则

\frac{a}{1} = a

= - 36 0^{\circ} n

= - 36 0^{\circ} n + \frac{1 5 ^{\circ}}{- 1}

\frac{1 5 ^{\circ}}{- 1} = - 1 5^{\circ}

\frac{1 5 ^{\circ}}{- 1}

使用分式法则:

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

= - \frac{1 5 ^{\circ}}{1}

使用分式法则:

\frac{a}{1} = a

\frac{1 5 ^{\circ}}{1} = 1 5^{\circ}

= - 1 5^{\circ}

= - 36 0^{\circ} n - 1 5^{\circ}

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

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

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

解

4 5^{\circ} - x = 30 0^{\circ} + 36 0^{\circ} n : x = - 36 0^{\circ} n - 25 5^{\circ}

4 5^{\circ} - x = 30 0^{\circ} + 36 0^{\circ} n

将

4 5^{\circ}

到右边

4 5^{\circ} - x = 30 0^{\circ} + 36 0^{\circ} n

两边减去

4 5^{\circ}

4 5^{\circ} - x - 4 5^{\circ} = 30 0^{\circ} + 36 0^{\circ} n - 4 5^{\circ}

化简

4 5^{\circ} - x - 4 5^{\circ} = 30 0^{\circ} + 36 0^{\circ} n - 4 5^{\circ}

化简

4 5^{\circ} - x - 4 5^{\circ} : - x

4 5^{\circ} - x - 4 5^{\circ}

同类项相加:

4 5^{\circ} - 4 5^{\circ} = 0

= - x

化简

30 0^{\circ} + 36 0^{\circ} n - 4 5^{\circ} : 36 0^{\circ} n + 25 5^{\circ}

30 0^{\circ} + 36 0^{\circ} n - 4 5^{\circ}

对同类项分组

= 36 0^{\circ} n - 4 5^{\circ} + 30 0^{\circ}

4, 3

的最小公倍数:

12

4, 3

最小公倍数 (LCM)

4

质因数分解:

2 \cdot 2

4

4

除以

24 = 2 \cdot 2

= 2 \cdot 2

3

质因数分解:

3

3

3

是质数，因此无法因数分解

= 3

将每个因子乘以它在

4

或

3

中出现的最多次数

= 2 \cdot 2 \cdot 3

数字相乘:

2 \cdot 2 \cdot 3 = 12

= 12

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

12

对于

4 5^{\circ} :

将分母和分子乘以

3

4 5^{\circ} = \frac{18 0 ^{\circ} 3}{4 \cdot 3} = 4 5^{\circ}

对于

30 0^{\circ} :

将分母和分子乘以

4

30 0^{\circ} = \frac{90 0 ^{\circ} 4}{3 \cdot 4} = 30 0^{\circ}

= - 4 5^{\circ} + 30 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} 3 + 360 0 ^{\circ}}{12}

同类项相加:

- 54 0^{\circ} + 360 0^{\circ} = 306 0^{\circ}

= 36 0^{\circ} n + 25 5^{\circ}

- x = 36 0^{\circ} n + 25 5^{\circ}

- x = 36 0^{\circ} n + 25 5^{\circ}

- x = 36 0^{\circ} n + 25 5^{\circ}

两边除以

- 1

- x = 36 0^{\circ} n + 25 5^{\circ}

两边除以

- 1

\frac{- x}{- 1} = \frac{36 0 ^{\circ} n}{- 1} + \frac{25 5 ^{\circ}}{- 1}

化简

\frac{- x}{- 1} = \frac{36 0 ^{\circ} n}{- 1} + \frac{25 5 ^{\circ}}{- 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{36 0 ^{\circ} n}{- 1} + \frac{25 5 ^{\circ}}{- 1} : - 36 0^{\circ} n - 25 5^{\circ}

\frac{36 0 ^{\circ} n}{- 1} + \frac{25 5 ^{\circ}}{- 1}

\frac{36 0 ^{\circ} n}{- 1} = - 36 0^{\circ} n

\frac{36 0 ^{\circ} n}{- 1}

使用分式法则:

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

= - \frac{36 0 ^{\circ} n}{1}

使用法则

\frac{a}{1} = a

= - 36 0^{\circ} n

= - 36 0^{\circ} n + \frac{25 5 ^{\circ}}{- 1}

\frac{25 5 ^{\circ}}{- 1} = - 25 5^{\circ}

\frac{25 5 ^{\circ}}{- 1}

使用分式法则:

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

= - \frac{25 5 ^{\circ}}{1}

使用分式法则:

\frac{a}{1} = a

\frac{25 5 ^{\circ}}{1} = 25 5^{\circ}

= - 25 5^{\circ}

= - 36 0^{\circ} n - 25 5^{\circ}

x = - 36 0^{\circ} n - 25 5^{\circ}

x = - 36 0^{\circ} n - 25 5^{\circ}

x = - 36 0^{\circ} n - 25 5^{\circ}

x = - 36 0^{\circ} n - 1 5^{\circ}, x = - 36 0^{\circ} n - 25 5^{\circ}

作图

流行的例子

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