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受欢迎的三角函数 >

cos(2x-30)=0

解答

cos (2 x - 3 0^{\circ}) = 0

解答

x = 18 0^{\circ} n + 6 0^{\circ}, x = 18 0^{\circ} n + 15 0^{\circ}

+1

弧度

x = \frac{π}{3} + πn, x = \frac{5 π}{6} + πn

求解步骤

cos (2 x - 3 0^{\circ}) = 0

cos (2 x - 3 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 - 3 0^{\circ} = 9 0^{\circ} + 36 0^{\circ} n, 2 x - 3 0^{\circ} = 27 0^{\circ} + 36 0^{\circ} n

2 x - 3 0^{\circ} = 9 0^{\circ} + 36 0^{\circ} n, 2 x - 3 0^{\circ} = 27 0^{\circ} + 36 0^{\circ} n

解

2 x - 3 0^{\circ} = 9 0^{\circ} + 36 0^{\circ} n : x = 18 0^{\circ} n + 6 0^{\circ}

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

将

3 0^{\circ}

到右边

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

两边加上

3 0^{\circ}

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

化简

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

化简

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

2 x - 3 0^{\circ} + 3 0^{\circ}

同类项相加:

- 3 0^{\circ} + 3 0^{\circ} = 0

= 2 x

化简

9 0^{\circ} + 36 0^{\circ} n + 3 0^{\circ} : 36 0^{\circ} n + 12 0^{\circ}

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

对同类项分组

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

2, 6

的最小公倍数:

6

2, 6

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

6

质因数分解:

2 \cdot 3

6

6

除以

26 = 3 \cdot 2

= 2 \cdot 3

2, 3

都是质数，因此无法进一步因数分解

= 2 \cdot 3

将每个因子乘以它在

2

或

6

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}

= 9 0^{\circ} + 3 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}}{6}

同类项相加:

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

= 12 0^{\circ}

约分:

2

= 36 0^{\circ} n + 12 0^{\circ}

2 x = 36 0^{\circ} n + 12 0^{\circ}

2 x = 36 0^{\circ} n + 12 0^{\circ}

2 x = 36 0^{\circ} n + 12 0^{\circ}

两边除以

2

2 x = 36 0^{\circ} n + 12 0^{\circ}

两边除以

2

\frac{2 x}{2} = \frac{36 0 ^{\circ} n}{2} + \frac{12 0 ^{\circ}}{2}

化简

\frac{2 x}{2} = \frac{36 0 ^{\circ} n}{2} + \frac{12 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{12 0 ^{\circ}}{2} : 18 0^{\circ} n + 6 0^{\circ}

\frac{36 0 ^{\circ} n}{2} + \frac{12 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{12 0 ^{\circ}}{2} = 6 0^{\circ}

\frac{12 0 ^{\circ}}{2}

使用分式法则:

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

= \frac{36 0 ^{\circ}}{3 \cdot 2}

数字相乘:

3 \cdot 2 = 6

= 6 0^{\circ}

约分:

2

= 6 0^{\circ}

= 18 0^{\circ} n + 6 0^{\circ}

x = 18 0^{\circ} n + 6 0^{\circ}

x = 18 0^{\circ} n + 6 0^{\circ}

x = 18 0^{\circ} n + 6 0^{\circ}

解

2 x - 3 0^{\circ} = 27 0^{\circ} + 36 0^{\circ} n : x = 18 0^{\circ} n + 15 0^{\circ}

2 x - 3 0^{\circ} = 27 0^{\circ} + 36 0^{\circ} n

将

3 0^{\circ}

到右边

2 x - 3 0^{\circ} = 27 0^{\circ} + 36 0^{\circ} n

两边加上

3 0^{\circ}

2 x - 3 0^{\circ} + 3 0^{\circ} = 27 0^{\circ} + 36 0^{\circ} n + 3 0^{\circ}

化简

2 x - 3 0^{\circ} + 3 0^{\circ} = 27 0^{\circ} + 36 0^{\circ} n + 3 0^{\circ}

化简

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

2 x - 3 0^{\circ} + 3 0^{\circ}

同类项相加:

- 3 0^{\circ} + 3 0^{\circ} = 0

= 2 x

化简

27 0^{\circ} + 36 0^{\circ} n + 3 0^{\circ} : 36 0^{\circ} n + 30 0^{\circ}

27 0^{\circ} + 36 0^{\circ} n + 3 0^{\circ}

对同类项分组

= 36 0^{\circ} n + 3 0^{\circ} + 27 0^{\circ}

6, 2

的最小公倍数:

6

6, 2

最小公倍数 (LCM)

6

质因数分解:

2 \cdot 3

6

6

除以

26 = 3 \cdot 2

= 2 \cdot 3

2, 3

都是质数，因此无法进一步因数分解

= 2 \cdot 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

6

或

2

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

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}

= 3 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} + 162 0 ^{\circ}}{6}

同类项相加:

18 0^{\circ} + 162 0^{\circ} = 180 0^{\circ}

= 30 0^{\circ}

约分:

2

= 36 0^{\circ} n + 30 0^{\circ}

2 x = 36 0^{\circ} n + 30 0^{\circ}

2 x = 36 0^{\circ} n + 30 0^{\circ}

2 x = 36 0^{\circ} n + 30 0^{\circ}

两边除以

2

2 x = 36 0^{\circ} n + 30 0^{\circ}

两边除以

2

\frac{2 x}{2} = \frac{36 0 ^{\circ} n}{2} + \frac{30 0 ^{\circ}}{2}

化简

\frac{2 x}{2} = \frac{36 0 ^{\circ} n}{2} + \frac{30 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{30 0 ^{\circ}}{2} : 18 0^{\circ} n + 15 0^{\circ}

\frac{36 0 ^{\circ} n}{2} + \frac{30 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{30 0 ^{\circ}}{2} = 15 0^{\circ}

\frac{30 0 ^{\circ}}{2}

使用分式法则:

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

= \frac{90 0 ^{\circ}}{3 \cdot 2}

数字相乘:

3 \cdot 2 = 6

= 15 0^{\circ}

= 18 0^{\circ} n + 15 0^{\circ}

x = 18 0^{\circ} n + 15 0^{\circ}

x = 18 0^{\circ} n + 15 0^{\circ}

x = 18 0^{\circ} n + 15 0^{\circ}

x = 18 0^{\circ} n + 6 0^{\circ}, x = 18 0^{\circ} n + 15 0^{\circ}

作图

流行的例子

sin (5 a) = 0

tan(x)cos(x)sin(x)-1=0

tan (x) cos (x) sin (x) - 1 = 0

7 tan (3 x) = 7

sin(θ)=((0.0543)/(0.9911))

sin (θ) = (\frac{0.0543}{0.9911})

sin (x) = 0.2419