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受欢迎的三角函数 >

(6(9.81)-6(9.81)sin(30))/(6+6)

解答

\frac{6 ( 9.81 ) - 6 ( 9.81 ) sin ( 3 0 ^{\circ} )}{6 + 6}

解答

\frac{981}{400}

+1

十进制

2.4525

求解步骤

\frac{6 ( 9.81 ) - 6 ( 9.81 ) sin ( 3 0 ^{\circ} )}{6 + 6}

= \frac{6 \cdot \frac{981}{100} - 6 \cdot \frac{981}{100} sin ( 3 0 ^{\circ} )}{6 + 6}

使用以下普通恒等式:

sin (3 0^{\circ}) = \frac{1}{2}

sin (3 0^{\circ})

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}

= \frac{1}{2}

= \frac{6 \cdot \frac{981}{100} - 6 \cdot \frac{981}{100} \cdot \frac{1}{2}}{6 + 6}

化简

\frac{6 \cdot \frac{981}{100} - 6 \cdot \frac{981}{100} \cdot \frac{1}{2}}{6 + 6} : \frac{981}{400}

\frac{6 \cdot \frac{981}{100} - 6 \cdot \frac{981}{100} \cdot \frac{1}{2}}{6 + 6}

数字相加:

6 + 6 = 12

= \frac{6 \cdot \frac{981}{100} - 6 \cdot \frac{1}{2} \cdot \frac{981}{100}}{12}

6 \cdot \frac{981}{100} = \frac{2943}{50}

6 \cdot \frac{981}{100}

分式相乘:

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

= \frac{981 \cdot 6}{100}

数字相乘:

981 \cdot 6 = 5886

= \frac{5886}{100}

约分:

2

= \frac{2943}{50}

6 \cdot \frac{981}{100} \cdot \frac{1}{2} = \frac{2943}{100}

6 \cdot \frac{981}{100} \cdot \frac{1}{2}

分式相乘:

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

= \frac{981 \cdot 1 \cdot 6}{100 \cdot 2}

数字相乘:

981 \cdot 1 \cdot 6 = 5886

= \frac{5886}{100 \cdot 2}

数字相乘:

100 \cdot 2 = 200

= \frac{5886}{200}

约分:

2

= \frac{2943}{100}

= \frac{\frac{2943}{50} - \frac{2943}{100}}{12}

化简

\frac{2943}{50} - \frac{2943}{100} : \frac{2943}{100}

\frac{2943}{50} - \frac{2943}{100}

50, 100

的最小公倍数:

100

50, 100

最小公倍数 (LCM)

50

质因数分解:

2 \cdot 5 \cdot 5

50

50

除以

250 = 25 \cdot 2

= 2 \cdot 25

25

除以

525 = 5 \cdot 5

= 2 \cdot 5 \cdot 5

2, 5

都是质数，因此无法进一步因数分解

= 2 \cdot 5 \cdot 5

100

质因数分解:

2 \cdot 2 \cdot 5 \cdot 5

100

100

除以

2100 = 50 \cdot 2

= 2 \cdot 50

50

除以

250 = 25 \cdot 2

= 2 \cdot 2 \cdot 25

25

除以

525 = 5 \cdot 5

= 2 \cdot 2 \cdot 5 \cdot 5

2, 5

都是质数，因此无法进一步因数分解

= 2 \cdot 2 \cdot 5 \cdot 5

将每个因子乘以它在

50

或

100

中出现的最多次数

= 2 \cdot 2 \cdot 5 \cdot 5

数字相乘:

2 \cdot 2 \cdot 5 \cdot 5 = 100

= 100

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

100

对于

\frac{2943}{50} :

将分母和分子乘以

2

\frac{2943}{50} = \frac{2943 \cdot 2}{50 \cdot 2} = \frac{5886}{100}

= \frac{5886}{100} - \frac{2943}{100}

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{5886 - 2943}{100}

数字相减:

5886 - 2943 = 2943

= \frac{2943}{100}

= \frac{\frac{2943}{100}}{12}

使用分式法则:

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

= \frac{2943}{100 \cdot 12}

数字相乘:

100 \cdot 12 = 1200

= \frac{2943}{1200}

约分:

3

= \frac{981}{400}

= \frac{981}{400}

流行的例子

arccos(-1/(sqrt(26)))

arccos (- \frac{1}{26})

sin (\frac{7}{12})

arccot(cot(-10))

arccot (cot (- 1 0^{\circ}))

cos(60)cos(65)-sin(60)sin(65)

cos (6 0^{\circ}) cos (6 5^{\circ}) - sin (6 0^{\circ}) sin (6 5^{\circ})

cos (\frac{37 π}{6})