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受欢迎的三角函数 >

sin((5pi)/(24))cos(pi/(24))

解答

sin (\frac{5 π}{24}) cos (\frac{π}{24})

解答

\frac{2 + 1}{4}

+1

十进制

0.60355 \dots

求解步骤

sin (\frac{5 π}{24}) cos (\frac{π}{24})

使用三角恒等式改写:

\frac{sin ( \frac{π}{4} ) + sin ( \frac{π}{6} )}{2}

sin (\frac{5 π}{24}) cos (\frac{π}{24})

使用积化和差恒等式:

sin (s) cos (t) = \frac{1}{2} (sin (s + t) + sin (s - t))

= \frac{1}{2} (sin (\frac{5 π}{24} + \frac{π}{24}) + sin (\frac{5 π}{24} - \frac{π}{24}))

化简:

\frac{5 π}{24} + \frac{π}{24} = \frac{π}{4}

\frac{5 π}{24} + \frac{π}{24}

使用法则

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

= \frac{5 π + π}{24}

同类项相加:

5 π + π = 6 π

= \frac{6 π}{24}

约分:

6

= \frac{π}{4}

化简:

\frac{5 π}{24} - \frac{π}{24} = \frac{π}{6}

\frac{5 π}{24} - \frac{π}{24}

使用法则

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

= \frac{5 π - π}{24}

同类项相加:

5 π - π = 4 π

= \frac{4 π}{24}

约分:

4

= \frac{π}{6}

\frac{1}{2} (sin (\frac{π}{4}) + sin (\frac{π}{6})) = \frac{sin ( \frac{π}{4} ) + sin ( \frac{π}{6} )}{2}

\frac{1}{2} (sin (\frac{π}{4}) + sin (\frac{π}{6}))

分式相乘:

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

= \frac{1 \cdot ( sin ( \frac{π}{4} ) + sin ( \frac{π}{6} ) )}{2}

1 \cdot (sin (\frac{π}{4}) + sin (\frac{π}{6})) = sin (\frac{π}{4}) + sin (\frac{π}{6})

1 \cdot (sin (\frac{π}{4}) + sin (\frac{π}{6}))

乘以:

1 \cdot (sin (\frac{π}{4}) + sin (\frac{π}{6})) = (sin (\frac{π}{4}) + sin (\frac{π}{6}))

= (sin (\frac{π}{4}) + sin (\frac{π}{6}))

去除括号:

(a) = a

= sin (\frac{π}{4}) + sin (\frac{π}{6})

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

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

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

使用以下普通恒等式:

sin (\frac{π}{4}) = \frac{2}{2}

sin (\frac{π}{4})

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{2}{2}

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}

= \frac{\frac{2}{2} + \frac{1}{2}}{2}

化简

\frac{\frac{2}{2} + \frac{1}{2}}{2} : \frac{2 + 1}{4}

\frac{\frac{2}{2} + \frac{1}{2}}{2}

合并分式

\frac{2}{2} + \frac{1}{2} : \frac{2 + 1}{2}

使用法则

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

= \frac{2 + 1}{2}

= \frac{\frac{2 + 1}{2}}{2}

使用分式法则:

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

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

数字相乘:

2 \cdot 2 = 4

= \frac{2 + 1}{4}

= \frac{2 + 1}{4}

流行的例子

2cos((5pi)/3)+cos^2((5pi)/3)

2 cos (\frac{5 π}{3}) + cos^{2} (\frac{5 π}{3})

sin (0.1 π)

sin (13. 5^{\circ})

- 2 sin (\frac{7 π}{4})

arcsin (\frac{10}{16})