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受欢迎的三角函数 >

sqrt(95^2+57.73^2-29557.73sin(30))

解答

9 5^{2} + 57.7 3^{2} - 2 \cdot 95 \cdot 57.73 sin (3 0^{\circ})

解答

\frac{68734029}{100}

+1

十进制

82.90598 \dots

求解步骤

9 5^{2} + 57.7 3^{2} - 2 \cdot 95 \cdot 57.73 sin (3 0^{\circ})

= 9 5^{2} + (\frac{5773}{100})^{2} - 2 \cdot 95 \cdot \frac{5773}{100} sin (3 0^{\circ})

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}

= 9 5^{2} + (\frac{5773}{100})^{2} - 2 \cdot 95 \cdot \frac{5773}{100} \cdot \frac{1}{2}

化简

9 5^{2} + (\frac{5773}{100})^{2} - 2 \cdot 95 \cdot \frac{5773}{100} \cdot \frac{1}{2} : \frac{68734029}{100}

9 5^{2} + (\frac{5773}{100})^{2} - 2 \cdot 95 \cdot \frac{5773}{100} \cdot \frac{1}{2}

(\frac{5773}{100})^{2} = \frac{577 3 ^{2}}{10 0 ^{2}}

(\frac{5773}{100})^{2}

使用指数法则:

(\frac{a}{b})^{c} = \frac{a ^{c}}{b ^{c}}

= \frac{577 3 ^{2}}{10 0 ^{2}}

2 \cdot 95 \cdot \frac{5773}{100} \cdot \frac{1}{2} = \frac{109687}{20}

2 \cdot 95 \cdot \frac{5773}{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{5773 \cdot 1 \cdot 2 \cdot 95}{100 \cdot 2}

约分:

2

= \frac{5773 \cdot 1 \cdot 95}{100}

数字相乘:

5773 \cdot 1 \cdot 95 = 548435

= \frac{548435}{100}

约分:

5

= \frac{109687}{20}

= 9 5^{2} + \frac{577 3 ^{2}}{10 0 ^{2}} - \frac{109687}{20}

9 5^{2} = 9025

9 5^{2}

9 5^{2} = 9025

= 9025

\frac{577 3 ^{2}}{10 0 ^{2}} = \frac{33327529}{10000}

\frac{577 3 ^{2}}{10 0 ^{2}}

577 3^{2} = 33327529

= \frac{33327529}{10 0 ^{2}}

10 0^{2} = 10000

= \frac{33327529}{10000}

= 9025 + \frac{33327529}{10000} - \frac{109687}{20}

化简

9025 + \frac{33327529}{10000} - \frac{109687}{20} : \frac{68734029}{10000}

9025 + \frac{33327529}{10000} - \frac{109687}{20}

将项转换为分式:

9025 = \frac{9025}{1}

= \frac{9025}{1} + \frac{33327529}{10000} - \frac{109687}{20}

1, 10000, 20

的最小公倍数:

10000

1, 10000, 20

最小公倍数 (LCM)

1

质因数分解

10000

质因数分解:

2 \cdot 2 \cdot 2 \cdot 2 \cdot 5 \cdot 5 \cdot 5 \cdot 5

10000

10000

除以

210000 = 5000 \cdot 2

= 2 \cdot 5000

5000

除以

25000 = 2500 \cdot 2

= 2 \cdot 2 \cdot 2500

2500

除以

22500 = 1250 \cdot 2

= 2 \cdot 2 \cdot 2 \cdot 1250

1250

除以

21250 = 625 \cdot 2

= 2 \cdot 2 \cdot 2 \cdot 2 \cdot 625

625

除以

5625 = 125 \cdot 5

= 2 \cdot 2 \cdot 2 \cdot 2 \cdot 5 \cdot 125

125

除以

5125 = 25 \cdot 5

= 2 \cdot 2 \cdot 2 \cdot 2 \cdot 5 \cdot 5 \cdot 25

25

除以

525 = 5 \cdot 5

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

20

质因数分解:

2 \cdot 2 \cdot 5

20

20

除以

220 = 10 \cdot 2

= 2 \cdot 10

10

除以

210 = 5 \cdot 2

= 2 \cdot 2 \cdot 5

2, 5

都是质数，因此无法进一步因数分解

= 2 \cdot 2 \cdot 5

计算出由至少在以下一个数字中出现的因数组成的数字:

1, 10000, 20

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

数字相乘:

2 \cdot 2 \cdot 2 \cdot 2 \cdot 5 \cdot 5 \cdot 5 \cdot 5 = 10000

= 10000

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

10000

对于

\frac{9025}{1} :

将分母和分子乘以

10000

\frac{9025}{1} = \frac{9025 \cdot 10000}{1 \cdot 10000} = \frac{90250000}{10000}

对于

\frac{109687}{20} :

将分母和分子乘以

500

\frac{109687}{20} = \frac{109687 \cdot 500}{20 \cdot 500} = \frac{54843500}{10000}

= \frac{90250000}{10000} + \frac{33327529}{10000} - \frac{54843500}{10000}

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{90250000 + 33327529 - 54843500}{10000}

数字相加/相减:

90250000 + 33327529 - 54843500 = 68734029

= \frac{68734029}{10000}

= \frac{68734029}{10000}

使用根式运算法则:

n \frac{a}{b} = \frac{n a}{n b},

假定

a \geq 0, b \geq 0

= \frac{68734029}{10000}

10000 = 100

10000

因式分解数字:

10000 = 10 0^{2}

= 10 0^{2}

使用根式运算法则:

n a^{n} = a

10 0^{2} = 100

= 100

= \frac{68734029}{100}

= \frac{68734029}{100}

流行的例子

18.84 - sin (3 π)

(arctan(3))/(10)

\frac{arctan ( 3 )}{10}

4.74-350.88(1-cos(0.142498))

4.74 - 350.88 (1 - cos (0.142498))

arcsin (0.494)

tan (32. 3^{\circ})