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受欢迎的三角函数 >

(1+cos(45))/(sin(45))

解答

\frac{1 + cos ( 4 5 ^{\circ} )}{sin ( 4 5 ^{\circ} )}

解答

2 + 1

+1

十进制

2.41421 \dots

求解步骤

\frac{1 + cos ( 4 5 ^{\circ} )}{sin ( 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}

使用以下普通恒等式:

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

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

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

化简

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

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

使用分式法则:

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

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

使用根式运算法则:

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

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

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

使用指数法则:

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

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

= 2^{- \frac{1}{2} + 1} (\frac{2}{2} + 1)

数字相减:

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

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

使用根式运算法则:

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

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

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

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

使用分配律:

a (b + c) = ab + a c

a = 2, b = 1, c = \frac{2}{2}

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

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

化简

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

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

因式分解出通项

2

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

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

1 + \frac{2}{2}

消掉

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

\frac{2}{2}

消掉

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

\frac{2}{2}

使用根式运算法则:

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

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

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

使用指数法则:

\frac{x ^{a}}{x ^{b}} = \frac{1}{x ^{b - a}}

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

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

数字相减:

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

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

使用根式运算法则:

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

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

= \frac{1}{2}

= \frac{1}{2}

= 1 + \frac{1}{2}

将项转换为分式:

1 = \frac{1 2}{2}

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

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{1 \cdot 2 + 1}{2}

乘以:

1 \cdot 2 = 2

= \frac{2 + 1}{2}

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

分式相乘:

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

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

约分:

2

= 2 + 1

= 2 + 1

= 2 + 1

流行的例子

arcsin (\frac{8}{12})

sin (60. 4^{\circ})

arccos (\frac{2}{2})

arctan((-12)/5)

arctan (\frac{- 12}{5})

arccos(cos((7pi)/8))

arccos (cos (\frac{7 π}{8}))