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受欢迎的三角函数 >

sin(x-30)cos(x-30)=(sqrt(3))/4

解答

sin (x - 3 0^{\circ}) cos (x - 3 0^{\circ}) = \frac{3}{4}

解答

x = 6 0^{\circ} + 18 0^{\circ} n, x = 18 0^{\circ} n + 9 0^{\circ}

+1

弧度

x = \frac{π}{3} + πn, x = \frac{π}{2} + πn

求解步骤

sin (x - 3 0^{\circ}) cos (x - 3 0^{\circ}) = \frac{3}{4}

使用三角恒等式改写

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

使用倍角公式:

2 sin (x) cos (x) = sin (2 x)

sin (x) cos (x) = \frac{sin ( 2 x )}{2}

= \frac{sin ( 2 ( - 3 0 ^{\circ} + x ) )}{2}

\frac{sin ( 2 ( - 3 0 ^{\circ} + x ) )}{2} = \frac{3}{4}

在两边乘以

2

\frac{sin ( 2 ( - 3 0 ^{\circ} + x ) )}{2} = \frac{3}{4}

在两边乘以

2

\frac{2 sin ( 2 ( - 3 0 ^{\circ} + x ) )}{2} = \frac{2 3}{4}

化简

sin (2 (- 3 0^{\circ} + x)) = \frac{3}{2}

sin (2 (- 3 0^{\circ} + x)) = \frac{3}{2}

sin (2 (- 3 0^{\circ} + x)) = \frac{3}{2}

的通解

sin (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} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{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} sin (x) 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2}

2 (- 3 0^{\circ} + x) = 6 0^{\circ} + 36 0^{\circ} n, 2 (- 3 0^{\circ} + x) = 12 0^{\circ} + 36 0^{\circ} n

2 (- 3 0^{\circ} + x) = 6 0^{\circ} + 36 0^{\circ} n, 2 (- 3 0^{\circ} + x) = 12 0^{\circ} + 36 0^{\circ} n

解

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

2 (- 3 0^{\circ} + x) = 6 0^{\circ} + 36 0^{\circ} n

两边除以

2

2 (- 3 0^{\circ} + x) = 6 0^{\circ} + 36 0^{\circ} n

两边除以

2

\frac{2 ( - 3 0 ^{\circ} + x )}{2} = \frac{6 0 ^{\circ}}{2} + \frac{36 0 ^{\circ} n}{2}

化简

\frac{2 ( - 3 0 ^{\circ} + x )}{2} = \frac{6 0 ^{\circ}}{2} + \frac{36 0 ^{\circ} n}{2}

化简

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

\frac{2 ( - 3 0 ^{\circ} + x )}{2}

数字相除:

\frac{2}{2} = 1

= - 3 0^{\circ} + x

化简

\frac{6 0 ^{\circ}}{2} + \frac{36 0 ^{\circ} n}{2} : 3 0^{\circ} + 18 0^{\circ} n

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

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

\frac{6 0 ^{\circ}}{2}

使用分式法则:

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

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

数字相乘:

3 \cdot 2 = 6

= 3 0^{\circ}

\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

= 3 0^{\circ} + 18 0^{\circ} n

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

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

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

将

3 0^{\circ}

到右边

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

两边加上

3 0^{\circ}

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

化简

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

化简

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

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

同类项相加:

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

= x

化简

3 0^{\circ} + 18 0^{\circ} n + 3 0^{\circ} : 6 0^{\circ} + 18 0^{\circ} n

3 0^{\circ} + 18 0^{\circ} n + 3 0^{\circ}

对同类项分组

= 3 0^{\circ} + 3 0^{\circ} + 18 0^{\circ} n

合并分式

3 0^{\circ} + 3 0^{\circ} : 6 0^{\circ}

使用法则

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

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

同类项相加:

18 0^{\circ} + 18 0^{\circ} = 36 0^{\circ}

= 6 0^{\circ}

约分:

2

= 6 0^{\circ}

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

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

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

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

解

2 (- 3 0^{\circ} + x) = 12 0^{\circ} + 36 0^{\circ} n : x = 18 0^{\circ} n + 9 0^{\circ}

2 (- 3 0^{\circ} + x) = 12 0^{\circ} + 36 0^{\circ} n

两边除以

2

2 (- 3 0^{\circ} + x) = 12 0^{\circ} + 36 0^{\circ} n

两边除以

2

\frac{2 ( - 3 0 ^{\circ} + x )}{2} = \frac{12 0 ^{\circ}}{2} + \frac{36 0 ^{\circ} n}{2}

化简

\frac{2 ( - 3 0 ^{\circ} + x )}{2} = \frac{12 0 ^{\circ}}{2} + \frac{36 0 ^{\circ} n}{2}

化简

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

\frac{2 ( - 3 0 ^{\circ} + x )}{2}

数字相除:

\frac{2}{2} = 1

= - 3 0^{\circ} + x

化简

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

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

\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}

\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

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

- 3 0^{\circ} + x = 6 0^{\circ} + 18 0^{\circ} n

- 3 0^{\circ} + x = 6 0^{\circ} + 18 0^{\circ} n

- 3 0^{\circ} + x = 6 0^{\circ} + 18 0^{\circ} n

将

3 0^{\circ}

到右边

- 3 0^{\circ} + x = 6 0^{\circ} + 18 0^{\circ} n

两边加上

3 0^{\circ}

- 3 0^{\circ} + x + 3 0^{\circ} = 6 0^{\circ} + 18 0^{\circ} n + 3 0^{\circ}

化简

- 3 0^{\circ} + x + 3 0^{\circ} = 6 0^{\circ} + 18 0^{\circ} n + 3 0^{\circ}

化简

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

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

同类项相加:

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

= x

化简

6 0^{\circ} + 18 0^{\circ} n + 3 0^{\circ} : 18 0^{\circ} n + 9 0^{\circ}

6 0^{\circ} + 18 0^{\circ} n + 3 0^{\circ}

对同类项分组

= 18 0^{\circ} n + 6 0^{\circ} + 3 0^{\circ}

3, 6

的最小公倍数:

6

3, 6

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

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

3

或

6

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}

= 6 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} 2 + 18 0 ^{\circ}}{6}

同类项相加:

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

= 9 0^{\circ}

约分:

3

= 18 0^{\circ} n + 9 0^{\circ}

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

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

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

x = 6 0^{\circ} + 18 0^{\circ} n, x = 18 0^{\circ} n + 9 0^{\circ}

作图

流行的例子

cos(θ)=-7/15 ,cos(θ/2),180<θ<270

cos (θ) = - \frac{7}{15}, cos (\frac{θ}{2}), 18 0^{\circ} < θ < 27 0^{\circ}

tan (\frac{x}{2}) = 4

-2sin(x)=-sqrt(2)

- 2 sin (x) = - 2

sin(pi-x)=cos((3pi)/2-x)+cos(pi)

sin (π - x) = cos (\frac{3 π}{2} - x) + cos (π)

4 csc (x) + 8 = 0