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受欢迎的三角函数 >

sin(60-x)-sin(60+x)=(sqrt(3))/2

解答

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

解答

x = - 6 0^{\circ} - 36 0^{\circ} n, x = - 12 0^{\circ} - 36 0^{\circ} n

+1

弧度

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

求解步骤

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

使用三角恒等式改写

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

使用和差化积恒等式:

sin (s) - sin (t) = 2 sin (\frac{s - t}{2}) cos (\frac{s + t}{2})

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

化简

2 sin (\frac{6 0 ^{\circ} - x - ( 6 0 ^{\circ} + x )}{2}) cos (\frac{6 0 ^{\circ} - x + 6 0 ^{\circ} + x}{2}) : sin (- x)

2 sin (\frac{6 0 ^{\circ} - x - ( 6 0 ^{\circ} + x )}{2}) cos (\frac{6 0 ^{\circ} - x + 6 0 ^{\circ} + x}{2})

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

\frac{6 0 ^{\circ} - x - ( 6 0 ^{\circ} + x )}{2}

化简

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

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

将项转换为分式:

x = \frac{x 3}{3}, (x + 6 0^{\circ}) = \frac{( 6 0 ^{\circ} + x ) 3}{3}

= 6 0^{\circ} - \frac{x \cdot 3}{3} - \frac{( 6 0 ^{\circ} + x ) \cdot 3}{3}

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} - x \cdot 3 - ( 6 0 ^{\circ} + x ) \cdot 3}{3}

乘开

18 0^{\circ} - x \cdot 3 - (6 0^{\circ} + x) \cdot 3 : - 6 x

18 0^{\circ} - x \cdot 3 - (6 0^{\circ} + x) \cdot 3

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

乘开

- 3 (6 0^{\circ} + x) : - 18 0^{\circ} - 3 x

- 3 (6 0^{\circ} + x)

使用分配律:

a (b + c) = ab + a c

a = - 3, b = 6 0^{\circ}, c = x

= - 3 \cdot 6 0^{\circ} + (- 3) x

使用加减运算法则

+ (- a) = - a

= - 3 \cdot 6 0^{\circ} - 3 x

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

3 \cdot 6 0^{\circ}

分式相乘:

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

= 18 0^{\circ}

约分:

3

= 18 0^{\circ}

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

= 18 0^{\circ} - x \cdot 3 - 18 0^{\circ} - 3 x

化简

18 0^{\circ} - x \cdot 3 - 18 0^{\circ} - 3 x : - 6 x

18 0^{\circ} - x \cdot 3 - 18 0^{\circ} - 3 x

对同类项分组

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

同类项相加:

- 3 x - 3 x = - 6 x

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

同类项相加:

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

= - 6 x

= - 6 x

= \frac{- 6 x}{3}

使用分式法则:

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

= - \frac{6 x}{3}

数字相除:

\frac{6}{3} = 2

= - 2 x

= \frac{- 2 x}{2}

使用分式法则:

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

= - \frac{2 x}{2}

数字相除:

\frac{2}{2} = 1

= - x

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

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

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

合并分式

6 0^{\circ} + 6 0^{\circ} : 12 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}}{3}

同类项相加:

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

= 12 0^{\circ}

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

同类项相加:

- x + x = 0

= \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}

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

化简

cos (6 0^{\circ}) : \frac{1}{2}

cos (6 0^{\circ})

使用以下普通恒等式:

cos (6 0^{\circ}) = \frac{1}{2}

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}

= \frac{1}{2}

= 2 \cdot \frac{1}{2} sin (- x)

分式相乘:

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

= \frac{1 \cdot 2}{2} sin (- x)

约分:

2

= sin (- x) \cdot 1

乘以:

sin (- x) \cdot 1 = sin (- x)

= sin (- x)

= sin (- x)

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

sin (- 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}

- x = 6 0^{\circ} + 36 0^{\circ} n, - x = 12 0^{\circ} + 36 0^{\circ} n

- x = 6 0^{\circ} + 36 0^{\circ} n, - x = 12 0^{\circ} + 36 0^{\circ} n

解

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

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

两边除以

- 1

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

两边除以

- 1

\frac{- x}{- 1} = \frac{6 0 ^{\circ}}{- 1} + \frac{36 0 ^{\circ} n}{- 1}

化简

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

\frac{6 0 ^{\circ}}{- 1} + \frac{36 0 ^{\circ} n}{- 1}

\frac{6 0 ^{\circ}}{- 1} = - 6 0^{\circ}

\frac{6 0 ^{\circ}}{- 1}

使用分式法则:

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

= - \frac{6 0 ^{\circ}}{1}

使用分式法则:

\frac{a}{1} = a

\frac{6 0 ^{\circ}}{1} = 6 0^{\circ}

= - 6 0^{\circ}

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

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

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

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

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

解

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

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

两边除以

- 1

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

两边除以

- 1

\frac{- x}{- 1} = \frac{12 0 ^{\circ}}{- 1} + \frac{36 0 ^{\circ} n}{- 1}

化简

\frac{- x}{- 1} = \frac{12 0 ^{\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{12 0 ^{\circ}}{- 1} + \frac{36 0 ^{\circ} n}{- 1} : - 12 0^{\circ} - 36 0^{\circ} n

\frac{12 0 ^{\circ}}{- 1} + \frac{36 0 ^{\circ} n}{- 1}

\frac{12 0 ^{\circ}}{- 1} = - 12 0^{\circ}

\frac{12 0 ^{\circ}}{- 1}

使用分式法则:

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

= - \frac{12 0 ^{\circ}}{1}

使用分式法则:

\frac{a}{1} = a

\frac{12 0 ^{\circ}}{1} = 12 0^{\circ}

= - 12 0^{\circ}

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

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

x = - 12 0^{\circ} - 36 0^{\circ} n

x = - 12 0^{\circ} - 36 0^{\circ} n

x = - 12 0^{\circ} - 36 0^{\circ} n

x = - 6 0^{\circ} - 36 0^{\circ} n, x = - 12 0^{\circ} - 36 0^{\circ} n

作图

流行的例子

tan(x/4)+sqrt(3)=0,0<= x<= 2pi

tan (\frac{x}{4}) + 3 = 0, 0 \leq x \leq 2 π

cot^{(2)}(x)-csc(x)-1=0

cot^{(2)} (x) - csc (x) - 1 = 0

4sin(x)+1=3csc(x)

4 sin (x) + 1 = 3 csc (x)

cos^2(x)-3sin(x)=0

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

csc(t)= 1/(-(sqrt(2))/2)

csc (t) = \frac{1}{- \frac{2}{2}}