zs

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

受欢迎的 >

cos(2x+60)=0

解答

cos (2 x + 6 0^{\circ}) = 0

解答

x = 18 0^{\circ} n + 1 5^{\circ}, x = 18 0^{\circ} n + 10 5^{\circ}

+1

弧度

x = \frac{π}{12} + πn, x = \frac{7 π}{12} + πn

求解步骤

cos (2 x + 6 0^{\circ}) = 0

cos (2 x + 6 0^{\circ}) = 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}

2 x + 6 0^{\circ} = 9 0^{\circ} + 36 0^{\circ} n, 2 x + 6 0^{\circ} = 27 0^{\circ} + 36 0^{\circ} n

2 x + 6 0^{\circ} = 9 0^{\circ} + 36 0^{\circ} n, 2 x + 6 0^{\circ} = 27 0^{\circ} + 36 0^{\circ} n

解

2 x + 6 0^{\circ} = 9 0^{\circ} + 36 0^{\circ} n : x = 18 0^{\circ} n + 1 5^{\circ}

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

将

6 0^{\circ}

到右边

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

两边减去

6 0^{\circ}

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

化简

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

化简

2 x + 6 0^{\circ} - 6 0^{\circ} : 2 x

2 x + 6 0^{\circ} - 6 0^{\circ}

同类项相加:

6 0^{\circ} - 6 0^{\circ} = 0

= 2 x

化简

9 0^{\circ} + 36 0^{\circ} n - 6 0^{\circ} : 36 0^{\circ} n + 3 0^{\circ}

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

对同类项分组

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

2, 3

的最小公倍数:

6

2, 3

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

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

2

或

3

中出现的最多次数

= 2 \cdot 3

数字相乘:

2 \cdot 3 = 6

= 6

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

6

对于

9 0^{\circ} :

将分母和分子乘以

3

9 0^{\circ} = \frac{18 0 ^{\circ} 3}{2 \cdot 3} = 9 0^{\circ}

对于

6 0^{\circ} :

将分母和分子乘以

2

6 0^{\circ} = \frac{18 0 ^{\circ} 2}{3 \cdot 2} = 6 0^{\circ}

= 9 0^{\circ} - 6 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 - 18 0 ^{\circ} 2}{6}

同类项相加:

54 0^{\circ} - 36 0^{\circ} = 18 0^{\circ}

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

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

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

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

两边除以

2

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

两边除以

2

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

化简

\frac{2 x}{2} = \frac{36 0 ^{\circ} n}{2} + \frac{3 0 ^{\circ}}{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{3 0 ^{\circ}}{2} : 18 0^{\circ} n + 1 5^{\circ}

\frac{36 0 ^{\circ} n}{2} + \frac{3 0 ^{\circ}}{2}

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

\frac{36 0 ^{\circ} n}{2}

数字相除:

\frac{2}{2} = 1

= 18 0^{\circ} n

\frac{3 0 ^{\circ}}{2} = 1 5^{\circ}

\frac{3 0 ^{\circ}}{2}

使用分式法则:

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

= \frac{18 0 ^{\circ}}{6 \cdot 2}

数字相乘:

6 \cdot 2 = 12

= 1 5^{\circ}

= 18 0^{\circ} n + 1 5^{\circ}

x = 18 0^{\circ} n + 1 5^{\circ}

x = 18 0^{\circ} n + 1 5^{\circ}

x = 18 0^{\circ} n + 1 5^{\circ}

解

2 x + 6 0^{\circ} = 27 0^{\circ} + 36 0^{\circ} n : x = 18 0^{\circ} n + 10 5^{\circ}

2 x + 6 0^{\circ} = 27 0^{\circ} + 36 0^{\circ} n

将

6 0^{\circ}

到右边

2 x + 6 0^{\circ} = 27 0^{\circ} + 36 0^{\circ} n

两边减去

6 0^{\circ}

2 x + 6 0^{\circ} - 6 0^{\circ} = 27 0^{\circ} + 36 0^{\circ} n - 6 0^{\circ}

化简

2 x + 6 0^{\circ} - 6 0^{\circ} = 27 0^{\circ} + 36 0^{\circ} n - 6 0^{\circ}

化简

2 x + 6 0^{\circ} - 6 0^{\circ} : 2 x

2 x + 6 0^{\circ} - 6 0^{\circ}

同类项相加:

6 0^{\circ} - 6 0^{\circ} = 0

= 2 x

化简

27 0^{\circ} + 36 0^{\circ} n - 6 0^{\circ} : 36 0^{\circ} n + 21 0^{\circ}

27 0^{\circ} + 36 0^{\circ} n - 6 0^{\circ}

对同类项分组

= 36 0^{\circ} n - 6 0^{\circ} + 27 0^{\circ}

3, 2

的最小公倍数:

6

3, 2

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

2

质因数分解:

2

2

2

是质数，因此无法因数分解

= 2

将每个因子乘以它在

3

或

2

中出现的最多次数

= 3 \cdot 2

数字相乘:

3 \cdot 2 = 6

= 6

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

6

对于

6 0^{\circ} :

将分母和分子乘以

2

6 0^{\circ} = \frac{18 0 ^{\circ} 2}{3 \cdot 2} = 6 0^{\circ}

对于

27 0^{\circ} :

将分母和分子乘以

3

27 0^{\circ} = \frac{54 0 ^{\circ} 3}{2 \cdot 3} = 27 0^{\circ}

= - 6 0^{\circ} + 27 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} 2 + 162 0 ^{\circ}}{6}

同类项相加:

- 36 0^{\circ} + 162 0^{\circ} = 126 0^{\circ}

= 36 0^{\circ} n + 21 0^{\circ}

2 x = 36 0^{\circ} n + 21 0^{\circ}

2 x = 36 0^{\circ} n + 21 0^{\circ}

2 x = 36 0^{\circ} n + 21 0^{\circ}

两边除以

2

2 x = 36 0^{\circ} n + 21 0^{\circ}

两边除以

2

\frac{2 x}{2} = \frac{36 0 ^{\circ} n}{2} + \frac{21 0 ^{\circ}}{2}

化简

\frac{2 x}{2} = \frac{36 0 ^{\circ} n}{2} + \frac{21 0 ^{\circ}}{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{21 0 ^{\circ}}{2} : 18 0^{\circ} n + 10 5^{\circ}

\frac{36 0 ^{\circ} n}{2} + \frac{21 0 ^{\circ}}{2}

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

\frac{36 0 ^{\circ} n}{2}

数字相除:

\frac{2}{2} = 1

= 18 0^{\circ} n

\frac{21 0 ^{\circ}}{2} = 10 5^{\circ}

\frac{21 0 ^{\circ}}{2}

使用分式法则:

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

= \frac{126 0 ^{\circ}}{6 \cdot 2}

数字相乘:

6 \cdot 2 = 12

= 10 5^{\circ}

= 18 0^{\circ} n + 10 5^{\circ}

x = 18 0^{\circ} n + 10 5^{\circ}

x = 18 0^{\circ} n + 10 5^{\circ}

x = 18 0^{\circ} n + 10 5^{\circ}

x = 18 0^{\circ} n + 1 5^{\circ}, x = 18 0^{\circ} n + 10 5^{\circ}

流行的例子

cos (θ) = 0.6596

-1=tan(x+pi/(18))

- 1 = tan (x + \frac{π}{18})

cos(x+60)=-sin(x)

cos (x + 6 0^{\circ}) = - sin (x)

cos^5(x)+cos(x)=2cos^2(x)

cos^{5} (x) + cos (x) = 2 cos^{2} (x)

sin(40+x)=cos(5x+10)

sin (4 0^{\circ} + x) = cos (5 x + 10)