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受欢迎的三角函数 >

6/(cos(45))

解答

\frac{6}{cos ( 4 5 ^{\circ} )}

解答

62

+1

十进制

8.48528 \dots

求解步骤

\frac{6}{cos ( 4 5 ^{\circ} )}

使用以下普通恒等式:

cos (4 5^{\circ}) = \frac{2}{2}

cos (4 5^{\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{2}{2}

= \frac{6}{\frac{2}{2}}

化简

\frac{6}{\frac{2}{2}} : 62

\frac{6}{\frac{2}{2}}

使用分式法则:

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

= \frac{6 \cdot 2}{2}

数字相乘:

6 \cdot 2 = 12

= \frac{12}{2}

分解

12 : 2^{2} \cdot 3

因式分解

12 = 2^{2} \cdot 3

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

消掉

\frac{2 ^{2} \cdot 3}{2} : 3 \cdot 2^{\frac{3}{2}}

\frac{2 ^{2} \cdot 3}{2}

使用根式运算法则:

n a = a^{\frac{1}{n}}

2 = 2^{\frac{1}{2}}

= \frac{2 ^{2} \cdot 3}{2 ^{\frac{1}{2}}}

使用指数法则:

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

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

= 3 \cdot 2^{- \frac{1}{2} + 2}

数字相减:

2 - \frac{1}{2} = \frac{3}{2}

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

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

2^{\frac{3}{2}} = 22

2^{\frac{3}{2}}

2^{\frac{3}{2}} = 2^{1 + \frac{1}{2}}

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

使用指数法则:

x^{a + b} = x^{a} x^{b}

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

整理后得

= 22

= 3 \cdot 22

数字相乘:

3 \cdot 2 = 6

= 62

= 62

流行的例子

2 cos (7 0^{\circ})

cos (2 π \cdot 0)

cos((sqrt(3))/3)

cos (\frac{3}{3})

- csc^{2} (1)

csc^{2} (3 0^{\circ})