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受欢迎的三角函数 >

sin(pi/(12))-sin((5pi)/(12))

解答

sin (\frac{π}{12}) - sin (\frac{5 π}{12})

解答

- \frac{2}{2}

+1

十进制

- 0.70710 \dots

求解步骤

sin (\frac{π}{12}) - sin (\frac{5 π}{12})

使用三角恒等式改写:

- 2 sin (\frac{π}{6}) cos (\frac{π}{4})

sin (\frac{π}{12}) - sin (\frac{5 π}{12})

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{\frac{π}{12} - \frac{5 π}{12}}{2}) cos (\frac{\frac{π}{12} + \frac{5 π}{12}}{2})

化简:

\frac{\frac{π}{12} - \frac{5 π}{12}}{2} = - \frac{π}{6}

\frac{\frac{π}{12} - \frac{5 π}{12}}{2}

合并分式

\frac{π}{12} - \frac{5 π}{12} : - \frac{π}{3}

使用法则

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

= \frac{π - 5 π}{12}

同类项相加:

π - 5 π = - 4 π

= \frac{- 4 π}{12}

使用分式法则:

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

= - \frac{4 π}{12}

约分:

4

= - \frac{π}{3}

= \frac{- \frac{π}{3}}{2}

使用分式法则:

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

= - \frac{\frac{π}{3}}{2}

使用分式法则:

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

\frac{\frac{π}{3}}{2} = \frac{π}{3 \cdot 2}

= - \frac{π}{3 \cdot 2}

数字相乘:

3 \cdot 2 = 6

= - \frac{π}{6}

化简:

\frac{\frac{π}{12} + \frac{5 π}{12}}{2} = \frac{π}{4}

\frac{\frac{π}{12} + \frac{5 π}{12}}{2}

合并分式

\frac{π}{12} + \frac{5 π}{12} : \frac{π}{2}

使用法则

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

= \frac{π + 5 π}{12}

同类项相加:

π + 5 π = 6 π

= \frac{6 π}{12}

约分:

6

= \frac{π}{2}

= \frac{\frac{π}{2}}{2}

使用分式法则:

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

= \frac{π}{2 \cdot 2}

数字相乘:

2 \cdot 2 = 4

= \frac{π}{4}

= 2 sin (- \frac{π}{6}) cos (\frac{π}{4})

利用以下特性:

sin (- x) = - sin (x)

sin (- \frac{π}{6}) = - sin (\frac{π}{6})

= 2 (- sin (\frac{π}{6})) cos (\frac{π}{4})

化简

= - 2 sin (\frac{π}{6}) cos (\frac{π}{4})

= - 2 sin (\frac{π}{6}) cos (\frac{π}{4})

使用以下普通恒等式:

sin (\frac{π}{6}) = \frac{1}{2}

sin (\frac{π}{6})

sin (x)

周期表（周期为

2 πn

"）：

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} sin (x) 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2}

= \frac{1}{2}

使用以下普通恒等式:

cos (\frac{π}{4}) = \frac{2}{2}

cos (\frac{π}{4})

cos (x)

周期表（周期为

2 πn

）：

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} cos (x) 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} cos (x) - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2}

= \frac{2}{2}

= - 2 \cdot \frac{1}{2} \cdot \frac{2}{2}

化简

- 2 \cdot \frac{1}{2} \cdot \frac{2}{2} : - \frac{2}{2}

- 2 \cdot \frac{1}{2} \cdot \frac{2}{2}

分式相乘:

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

= - \frac{1 \cdot 2 \cdot 2}{2 \cdot 2}

约分:

2

= - \frac{1 \cdot 2}{2}

乘以:

1 \cdot 2 = 2

= - \frac{2}{2}

= - \frac{2}{2}

流行的例子

arcsin(1/2)+arcsin((sqrt(3))/2)

arcsin (\frac{1}{2}) + arcsin (\frac{3}{2})

csc(arccos((sqrt(21))/7))

csc (arccos (\frac{21}{7}))

cos (2 \frac{3 π}{4})

- ln ∣ cos (0) ∣

tan (- \frac{7 π}{2})