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受欢迎的三角函数 >

(sec(330))/(cot(210))

解答

\frac{sec ( 33 0 ^{\circ} )}{cot ( 21 0 ^{\circ} )}

解答

\frac{2}{3}

+1

十进制

0.66666 \dots

求解步骤

\frac{sec ( 33 0 ^{\circ} )}{cot ( 21 0 ^{\circ} )}

使用三角恒等式改写:

sec (33 0^{\circ}) = \frac{2 3}{3}

sec (33 0^{\circ})

使用三角恒等式改写:

\frac{1}{cos ( 33 0 ^{\circ} )}

sec (33 0^{\circ})

使用基本三角恒等式:

sec (x) = \frac{1}{cos ( x )}

= \frac{1}{cos ( 33 0 ^{\circ} )}

= \frac{1}{cos ( 33 0 ^{\circ} )}

使用三角恒等式改写:

cos (33 0^{\circ}) = \frac{3}{2}

cos (33 0^{\circ})

使用三角恒等式改写:

cos (18 0^{\circ}) cos (15 0^{\circ}) - sin (18 0^{\circ}) sin (15 0^{\circ})

cos (33 0^{\circ})

将

cos (33 0^{\circ})

写为

cos (18 0^{\circ} + 15 0^{\circ})

= cos (18 0^{\circ} + 15 0^{\circ})

使用角和恒等式:

cos (s + t) = cos (s) cos (t) - sin (s) sin (t)

= cos (18 0^{\circ}) cos (15 0^{\circ}) - sin (18 0^{\circ}) sin (15 0^{\circ})

= cos (18 0^{\circ}) cos (15 0^{\circ}) - sin (18 0^{\circ}) sin (15 0^{\circ})

使用以下普通恒等式:

cos (18 0^{\circ}) = (- 1)

cos (18 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}

= (- 1)

使用以下普通恒等式:

cos (15 0^{\circ}) = - \frac{3}{2}

cos (15 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{3}{2}

使用以下普通恒等式:

sin (18 0^{\circ}) = 0

sin (18 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}

= 0

使用以下普通恒等式:

sin (15 0^{\circ}) = \frac{1}{2}

sin (15 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}

= (- 1) (- \frac{3}{2}) - 0 \cdot \frac{1}{2}

化简

= \frac{3}{2}

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

化简

\frac{1}{\frac{3}{2}} : \frac{2 3}{3}

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

使用分式法则:

\frac{1}{\frac{b}{c}} = \frac{c}{b}

= \frac{2}{3}

\frac{2}{3}

有理化:

\frac{2 3}{3}

\frac{2}{3}

乘以共轭根式

\frac{3}{3}

= \frac{2 3}{3 3}

33 = 3

33

使用根式运算法则:

a a = a

33 = 3

= 3

= \frac{2 3}{3}

= \frac{2 3}{3}

= \frac{2 3}{3}

使用三角恒等式改写:

cot (21 0^{\circ}) = 3

cot (21 0^{\circ})

cot (21 0^{\circ}) = cot (3 0^{\circ})

cot (21 0^{\circ})

将

21 0^{\circ}

改写为

18 0^{\circ} + 3 0^{\circ}

= cot (18 0^{\circ} + 3 0^{\circ})

使用周期

cot

:

cot (x + 18 0^{\circ}) = cot (x)

cot (18 0^{\circ} + 3 0^{\circ}) = cot (3 0^{\circ})

= cot (3 0^{\circ})

= cot (3 0^{\circ})

使用以下普通恒等式:

cot (3 0^{\circ}) = 3

cot (3 0^{\circ})

cot (x)

周期表（周期为

18 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} cot (x) \mp \infty 31 \frac{3}{3} 0 - \frac{3}{3} - 1 - 3

= 3

= 3

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

化简

\frac{\frac{2 3}{3}}{3} : \frac{2}{3}

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

使用分式法则:

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

= \frac{2 3}{3 3}

\frac{2 3}{3 3}

有理化:

\frac{2}{3}

\frac{2 3}{3 3}

乘以共轭根式

\frac{3}{3}

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

233 = 6

233

使用根式运算法则:

a a = a

33 = 3

= 2 \cdot 3

数字相乘:

2 \cdot 3 = 6

= 6

333 = 9

333

使用指数法则:

a^{b} \cdot a^{c} = a^{b + c}

333 = 3 \cdot 3^{\frac{1}{2}} \cdot 3^{\frac{1}{2}} = 3^{1 + \frac{1}{2} + \frac{1}{2}}

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

同类项相加:

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

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

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

2 \cdot \frac{1}{2}

分式相乘:

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

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

约分:

2

= 1

= 3^{1 + 1}

数字相加:

1 + 1 = 2

= 3^{2}

3^{2} = 9

= 9

= \frac{6}{9}

约分:

3

= \frac{2}{3}

= \frac{2}{3}

= \frac{2}{3}

流行的例子

(7sin(0.001))/((0.001))

\frac{7 sin ( 0.001 )}{( 0.001 )}

(7.55*sin(70))/(sin(40))

\frac{7.55 \cdot sin ( 7 0 ^{\circ} )}{sin ( 4 0 ^{\circ} )}

1+2cos((2pi)/3)

1 + 2 cos (\frac{2 π}{3})

50 (3 + 3 cos (5 3^{\circ}))

arctan (1.3333)