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受欢迎的三角函数 >

(cos(pi/6))/((1-sin(pi/6))^2)

解答

\frac{cos ( \frac{π}{6} )}{( 1 - sin ( \frac{π}{6} ) ) ^{2}}

解答

23

+1

十进制

3.46410 \dots

求解步骤

\frac{cos ( \frac{π}{6} )}{( 1 - sin ( \frac{π}{6} ) ) ^{2}}

使用以下普通恒等式:

cos (\frac{π}{6}) = \frac{3}{2}

cos (\frac{π}{6})

cos (x)

周期表（周期为

2 πn

）：

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} cos (x) 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} cos (x) - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2}

= \frac{3}{2}

使用以下普通恒等式:

sin (\frac{π}{6}) = \frac{1}{2}

sin (\frac{π}{6})

sin (x)

周期表（周期为

2 πn

"）：

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} 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{\frac{3}{2}}{( 1 - \frac{1}{2} ) ^{2}}

化简

\frac{\frac{3}{2}}{( 1 - \frac{1}{2} ) ^{2}} : 23

\frac{\frac{3}{2}}{( 1 - \frac{1}{2} ) ^{2}}

使用分式法则:

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

= \frac{3}{2 ( 1 - \frac{1}{2} ) ^{2}}

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

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

化简

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

1 - \frac{1}{2}

将项转换为分式:

1 = \frac{1 \cdot 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}

1 \cdot 2 - 1 = 1

1 \cdot 2 - 1

数字相乘:

1 \cdot 2 = 2

= 2 - 1

数字相减:

2 - 1 = 1

= 1

= \frac{1}{2}

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

使用指数法则:

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

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

使用法则

1^{a} = 1

1^{2} = 1

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

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

乘

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

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

分式相乘:

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

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

数字相乘:

1 \cdot 2 = 2

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

约分:

2

= \frac{1}{2}

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

使用分式法则:

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

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

使用法则

\frac{a}{1} = a

= 23

= 23

流行的例子

sech^{2} (1)

3arctan(1/7)+2arctan(2/11)

3 arctan (\frac{1}{7}) + 2 arctan (\frac{2}{11})

ln(sec(pi/2)+tan(pi/2))

ln (sec (\frac{π}{2}) + tan (\frac{π}{2}))

sin^{2} (8)

sin (6 7^{\circ}) (\frac{1}{2})^{\circ}