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受欢迎的三角函数 >

sqrt((100^2+120^2-2100120*cos(60)))

解答

(10 0^{2} + 12 0^{2} - 2 \cdot 100 \cdot 120 \cdot cos (6 0^{\circ}))

解答

2031

+1

十进制

111.35528 \dots

求解步骤

(10 0^{2} + 12 0^{2} - 2 \cdot 100 \cdot 120 cos (6 0^{\circ}))

= 10 0^{2} + 12 0^{2} - 2 \cdot 100 \cdot 120 cos (6 0^{\circ})

使用以下普通恒等式:

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

cos (6 0^{\circ})

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}

= 10 0^{2} + 12 0^{2} - 2 \cdot 100 \cdot 120 \cdot \frac{1}{2}

化简

10 0^{2} + 12 0^{2} - 2 \cdot 100 \cdot 120 \cdot \frac{1}{2} : 2031

10 0^{2} + 12 0^{2} - 2 \cdot 100 \cdot 120 \cdot \frac{1}{2}

2 \cdot 100 \cdot 120 \cdot \frac{1}{2} = 12000

2 \cdot 100 \cdot 120 \cdot \frac{1}{2}

分式相乘:

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

= \frac{1 \cdot 2 \cdot 100 \cdot 120}{2}

约分:

2

= 1 \cdot 100 \cdot 120

数字相乘:

1 \cdot 100 \cdot 120 = 12000

= 12000

= 10 0^{2} + 12 0^{2} - 12000

10 0^{2} = 10000

= 10000 + 12 0^{2} - 12000

12 0^{2} = 14400

= 10000 + 14400 - 12000

数字相加/相减:

10000 + 14400 - 12000 = 12400

= 12400

12400

质因数分解:

2^{4} \cdot 5^{2} \cdot 31

12400

12400

除以

212400 = 6200 \cdot 2

= 2 \cdot 6200

6200

除以

26200 = 3100 \cdot 2

= 2 \cdot 2 \cdot 3100

3100

除以

23100 = 1550 \cdot 2

= 2 \cdot 2 \cdot 2 \cdot 1550

1550

除以

21550 = 775 \cdot 2

= 2 \cdot 2 \cdot 2 \cdot 2 \cdot 775

775

除以

5775 = 155 \cdot 5

= 2 \cdot 2 \cdot 2 \cdot 2 \cdot 5 \cdot 155

155

除以

5155 = 31 \cdot 5

= 2 \cdot 2 \cdot 2 \cdot 2 \cdot 5 \cdot 5 \cdot 31

2, 5, 31

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 31

= 2^{4} \cdot 5^{2} \cdot 31

= 2^{4} \cdot 5^{2} \cdot 31

使用根式运算法则:

n ab = n a n b

= 31 2^{4} 5^{2}

使用根式运算法则:

n a^{m} = a^{\frac{m}{n}}

2^{4} = 2^{\frac{4}{2}} = 2^{2}

= 2^{2} 31 5^{2}

使用根式运算法则:

n a^{n} = a

5^{2} = 5

= 2^{2} \cdot 531

整理后得

= 2031

= 2031

流行的例子

5 \cdot cos (5 3^{\circ})

arctan(4/(sqrt(3)))

arctan (\frac{4}{3})

arcsin (\frac{2}{10})

limit as x approaches infinity of arctan(x/2)

x \to \infty lim (arctan (\frac{x}{2}))

\frac{1}{cos ( 0.5 )}