zs

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

受欢迎的三角函数 >

(2.7*10^{-4})(9.8)tan(36)

解答

(2.7 \cdot 1 0^{- 4}) (9.8) tan (3 6^{\circ})

解答

\frac{1323 2 ( 5 - 1 ) 5 - 5}{2000000}

+1

十进制

0.00192 \dots

求解步骤

(2.7 \cdot 1 0^{- 4}) (9.8) tan (3 6^{\circ})

= \frac{27}{10} \cdot 1 0^{- 4} \cdot \frac{49}{5} tan (3 6^{\circ})

使用三角恒等式改写:

tan (3 6^{\circ}) = \frac{2 ( 5 - 1 ) 5 - 5}{4}

tan (3 6^{\circ})

使用三角恒等式改写:

\frac{sin ( 3 6 ^{\circ} )}{cos ( 3 6 ^{\circ} )}

tan (3 6^{\circ})

使用基本三角恒等式:

tan (x) = \frac{sin ( x )}{cos ( x )}

= \frac{sin ( 3 6 ^{\circ} )}{cos ( 3 6 ^{\circ} )}

= \frac{sin ( 3 6 ^{\circ} )}{cos ( 3 6 ^{\circ} )}

使用三角恒等式改写:

sin (3 6^{\circ}) = \frac{2 5 - 5}{4}

sin (3 6^{\circ})

显示:

cos (3 6^{\circ}) - sin (1 8^{\circ}) = \frac{1}{2}

使用以下积化和差公式:

2 sin (x) cos (y) = sin (x + y) - sin (x - y)

2 cos (3 6^{\circ}) sin (1 8^{\circ}) = sin (5 4^{\circ}) - sin (1 8^{\circ})

显示:

2 cos (3 6^{\circ}) sin (1 8^{\circ}) = \frac{1}{2}

使用倍角公式:

sin (2 x) = 2 sin (x) cos (x)

sin (7 2^{\circ}) = 2 sin (3 6^{\circ}) cos (3 6^{\circ})

sin (7 2^{\circ}) sin (3 6^{\circ}) = 4 sin (3 6^{\circ}) sin (1 8^{\circ}) cos (3 6^{\circ}) cos (1 8^{\circ})

两边除以

sin (3 6^{\circ})

sin (7 2^{\circ}) = 4 sin (1 8^{\circ}) cos (3 6^{\circ}) cos (1 8^{\circ})

利用以下特性:

sin (x) = cos (9 0^{\circ} - x)

sin (7 2^{\circ}) = cos (9 0^{\circ} - 7 2^{\circ})

cos (9 0^{\circ} - 7 2^{\circ}) = 4 sin (1 8^{\circ}) cos (3 6^{\circ}) cos (1 8^{\circ})

cos (1 8^{\circ}) = 4 sin (1 8^{\circ}) cos (3 6^{\circ}) cos (1 8^{\circ})

两边除以

cos (1 8^{\circ})

1 = 4 sin (1 8^{\circ}) cos (3 6^{\circ})

两边除以

2

\frac{1}{2} = 2 sin (1 8^{\circ}) cos (3 6^{\circ})

代入

\frac{1}{2} = 2 sin (1 8^{\circ}) cos (3 6^{\circ})

\frac{1}{2} = sin (5 4^{\circ}) - sin (1 8^{\circ})

sin (5 4^{\circ}) = cos (9 0^{\circ} - 5 4^{\circ})

\frac{1}{2} = cos (9 0^{\circ} - 5 4^{\circ}) - sin (1 8^{\circ})

\frac{1}{2} = cos (3 6^{\circ}) - sin (1 8^{\circ})

显示:

cos (3 6^{\circ}) + sin (1 8^{\circ}) = \frac{5}{4}

使用因式分解法则:

a^{2} - b^{2} = (a + b) (a - b)

a = cos (3 6^{\circ}) + sin (1 8^{\circ})

(cos (3 6^{\circ}) + sin (1 8^{\circ}))^{2} - (cos (3 6^{\circ}) - sin (1 8^{\circ}))^{2} = ((cos (3 6^{\circ}) + sin (1 8^{\circ})) + (cos (3 6^{\circ}) - sin (1 8^{\circ}))) ((cos (3 6^{\circ}) + sin (1 8^{\circ})) - (cos (3 6^{\circ}) - sin (1 8^{\circ})))

整理后得

(cos (3 6^{\circ}) + sin (1 8^{\circ}))^{2} - (cos (3 6^{\circ}) - sin (1 8^{\circ}))^{2} = 2 (2 cos (3 6^{\circ}) sin (1 8^{\circ}))

显示:

2 cos (3 6^{\circ}) sin (1 8^{\circ}) = \frac{1}{2}

使用倍角公式:

sin (2 x) = 2 sin (x) cos (x)

sin (7 2^{\circ}) = 2 sin (3 6^{\circ}) cos (3 6^{\circ})

sin (7 2^{\circ}) sin (3 6^{\circ}) = 4 sin (3 6^{\circ}) sin (1 8^{\circ}) cos (3 6^{\circ}) cos (1 8^{\circ})

两边除以

sin (3 6^{\circ})

sin (7 2^{\circ}) = 4 sin (1 8^{\circ}) cos (3 6^{\circ}) cos (1 8^{\circ})

利用以下特性:

sin (x) = cos (9 0^{\circ} - x)

sin (7 2^{\circ}) = cos (9 0^{\circ} - 7 2^{\circ})

cos (9 0^{\circ} - 7 2^{\circ}) = 4 sin (1 8^{\circ}) cos (3 6^{\circ}) cos (1 8^{\circ})

cos (1 8^{\circ}) = 4 sin (1 8^{\circ}) cos (3 6^{\circ}) cos (1 8^{\circ})

两边除以

cos (1 8^{\circ})

1 = 4 sin (1 8^{\circ}) cos (3 6^{\circ})

两边除以

2

\frac{1}{2} = 2 sin (1 8^{\circ}) cos (3 6^{\circ})

代入

2 cos (3 6^{\circ}) sin (1 8^{\circ}) = \frac{1}{2}

(cos (3 6^{\circ}) + sin (1 8^{\circ}))^{2} - (cos (3 6^{\circ}) - sin (1 8^{\circ}))^{2} = 1

代入

cos (3 6^{\circ}) - sin (1 8^{\circ}) = \frac{1}{2}

(cos (3 6^{\circ}) + sin (1 8^{\circ}))^{2} - (\frac{1}{2})^{2} = 1

整理后得

(cos (3 6^{\circ}) + sin (1 8^{\circ}))^{2} - \frac{1}{4} = 1

两边加上

\frac{1}{4}

(cos (3 6^{\circ}) + sin (1 8^{\circ}))^{2} - \frac{1}{4} + \frac{1}{4} = 1 + \frac{1}{4}

整理后得

(cos (3 6^{\circ}) + sin (1 8^{\circ}))^{2} = \frac{5}{4}

在两侧开平方

cos (3 6^{\circ}) + sin (1 8^{\circ}) = \pm \frac{5}{4}

cos (3 6^{\circ})

不能为负

sin (1 8^{\circ})

不能为负

cos (3 6^{\circ}) + sin (1 8^{\circ}) = \frac{5}{4}

以下方程式相加

cos (3 6^{\circ}) + sin (1 8^{\circ}) = \frac{5}{2}

((cos (3 6^{\circ}) + sin (1 8^{\circ})) + (cos (3 6^{\circ}) - sin (1 8^{\circ}))) = (\frac{5}{2} + \frac{1}{2})

整理后得

cos (3 6^{\circ}) = \frac{5 + 1}{4}

两边进行平方

(cos (3 6^{\circ}))^{2} = (\frac{5 + 1}{4})^{2}

利用以下特性:

sin^{2} (x) = 1 - cos^{2} (x)

sin^{2} (3 6^{\circ}) = 1 - cos^{2} (3 6^{\circ})

代入

cos (3 6^{\circ}) = \frac{5 + 1}{4}

sin^{2} (3 6^{\circ}) = 1 - (\frac{5 + 1}{4})^{2}

整理后得

sin^{2} (3 6^{\circ}) = \frac{5 - 5}{8}

在两侧开平方

sin (3 6^{\circ}) = \pm \frac{5 - 5}{8}

sin (3 6^{\circ})

不能为负

sin (3 6^{\circ}) = \frac{5 - 5}{8}

整理后得

sin (3 6^{\circ}) = \frac{\frac{5 - 5}{2}}{2}

= \frac{\frac{5 - 5}{2}}{2}

化简

= \frac{2 5 - 5}{4}

使用三角恒等式改写:

cos (3 6^{\circ}) = \frac{5 + 1}{4}

cos (3 6^{\circ})

显示:

cos (3 6^{\circ}) - sin (1 8^{\circ}) = \frac{1}{2}

使用以下积化和差公式:

2 sin (x) cos (y) = sin (x + y) - sin (x - y)

2 cos (3 6^{\circ}) sin (1 8^{\circ}) = sin (5 4^{\circ}) - sin (1 8^{\circ})

显示:

2 cos (3 6^{\circ}) sin (1 8^{\circ}) = \frac{1}{2}

使用倍角公式:

sin (2 x) = 2 sin (x) cos (x)

sin (7 2^{\circ}) = 2 sin (3 6^{\circ}) cos (3 6^{\circ})

sin (7 2^{\circ}) sin (3 6^{\circ}) = 4 sin (3 6^{\circ}) sin (1 8^{\circ}) cos (3 6^{\circ}) cos (1 8^{\circ})

两边除以

sin (3 6^{\circ})

sin (7 2^{\circ}) = 4 sin (1 8^{\circ}) cos (3 6^{\circ}) cos (1 8^{\circ})

利用以下特性:

sin (x) = cos (9 0^{\circ} - x)

sin (7 2^{\circ}) = cos (9 0^{\circ} - 7 2^{\circ})

cos (9 0^{\circ} - 7 2^{\circ}) = 4 sin (1 8^{\circ}) cos (3 6^{\circ}) cos (1 8^{\circ})

cos (1 8^{\circ}) = 4 sin (1 8^{\circ}) cos (3 6^{\circ}) cos (1 8^{\circ})

两边除以

cos (1 8^{\circ})

1 = 4 sin (1 8^{\circ}) cos (3 6^{\circ})

两边除以

2

\frac{1}{2} = 2 sin (1 8^{\circ}) cos (3 6^{\circ})

代入

\frac{1}{2} = 2 sin (1 8^{\circ}) cos (3 6^{\circ})

\frac{1}{2} = sin (5 4^{\circ}) - sin (1 8^{\circ})

sin (5 4^{\circ}) = cos (9 0^{\circ} - 5 4^{\circ})

\frac{1}{2} = cos (9 0^{\circ} - 5 4^{\circ}) - sin (1 8^{\circ})

\frac{1}{2} = cos (3 6^{\circ}) - sin (1 8^{\circ})

显示:

cos (3 6^{\circ}) + sin (1 8^{\circ}) = \frac{5}{4}

使用因式分解法则:

a^{2} - b^{2} = (a + b) (a - b)

a = cos (3 6^{\circ}) + sin (1 8^{\circ})

(cos (3 6^{\circ}) + sin (1 8^{\circ}))^{2} - (cos (3 6^{\circ}) - sin (1 8^{\circ}))^{2} = ((cos (3 6^{\circ}) + sin (1 8^{\circ})) + (cos (3 6^{\circ}) - sin (1 8^{\circ}))) ((cos (3 6^{\circ}) + sin (1 8^{\circ})) - (cos (3 6^{\circ}) - sin (1 8^{\circ})))

整理后得

(cos (3 6^{\circ}) + sin (1 8^{\circ}))^{2} - (cos (3 6^{\circ}) - sin (1 8^{\circ}))^{2} = 2 (2 cos (3 6^{\circ}) sin (1 8^{\circ}))

显示:

2 cos (3 6^{\circ}) sin (1 8^{\circ}) = \frac{1}{2}

使用倍角公式:

sin (2 x) = 2 sin (x) cos (x)

sin (7 2^{\circ}) = 2 sin (3 6^{\circ}) cos (3 6^{\circ})

sin (7 2^{\circ}) sin (3 6^{\circ}) = 4 sin (3 6^{\circ}) sin (1 8^{\circ}) cos (3 6^{\circ}) cos (1 8^{\circ})

两边除以

sin (3 6^{\circ})

sin (7 2^{\circ}) = 4 sin (1 8^{\circ}) cos (3 6^{\circ}) cos (1 8^{\circ})

利用以下特性:

sin (x) = cos (9 0^{\circ} - x)

sin (7 2^{\circ}) = cos (9 0^{\circ} - 7 2^{\circ})

cos (9 0^{\circ} - 7 2^{\circ}) = 4 sin (1 8^{\circ}) cos (3 6^{\circ}) cos (1 8^{\circ})

cos (1 8^{\circ}) = 4 sin (1 8^{\circ}) cos (3 6^{\circ}) cos (1 8^{\circ})

两边除以

cos (1 8^{\circ})

1 = 4 sin (1 8^{\circ}) cos (3 6^{\circ})

两边除以

2

\frac{1}{2} = 2 sin (1 8^{\circ}) cos (3 6^{\circ})

代入

2 cos (3 6^{\circ}) sin (1 8^{\circ}) = \frac{1}{2}

(cos (3 6^{\circ}) + sin (1 8^{\circ}))^{2} - (cos (3 6^{\circ}) - sin (1 8^{\circ}))^{2} = 1

代入

cos (3 6^{\circ}) - sin (1 8^{\circ}) = \frac{1}{2}

(cos (3 6^{\circ}) + sin (1 8^{\circ}))^{2} - (\frac{1}{2})^{2} = 1

整理后得

(cos (3 6^{\circ}) + sin (1 8^{\circ}))^{2} - \frac{1}{4} = 1

两边加上

\frac{1}{4}

(cos (3 6^{\circ}) + sin (1 8^{\circ}))^{2} - \frac{1}{4} + \frac{1}{4} = 1 + \frac{1}{4}

整理后得

(cos (3 6^{\circ}) + sin (1 8^{\circ}))^{2} = \frac{5}{4}

在两侧开平方

cos (3 6^{\circ}) + sin (1 8^{\circ}) = \pm \frac{5}{4}

cos (3 6^{\circ})

不能为负

sin (1 8^{\circ})

不能为负

cos (3 6^{\circ}) + sin (1 8^{\circ}) = \frac{5}{4}

以下方程式相加

cos (3 6^{\circ}) + sin (1 8^{\circ}) = \frac{5}{2}

((cos (3 6^{\circ}) + sin (1 8^{\circ})) + (cos (3 6^{\circ}) - sin (1 8^{\circ}))) = (\frac{5}{2} + \frac{1}{2})

整理后得

cos (3 6^{\circ}) = \frac{5 + 1}{4}

= \frac{5 + 1}{4}

= \frac{\frac{2 5 - 5}{4}}{\frac{5 + 1}{4}}

化简

\frac{\frac{2 5 - 5}{4}}{\frac{5 + 1}{4}} : \frac{2 ( 5 - 1 ) 5 - 5}{4}

\frac{\frac{2 5 - 5}{4}}{\frac{5 + 1}{4}}

分式相除:

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

= \frac{2 5 - 5 \cdot 4}{4 ( 5 + 1 )}

约分:

4

= \frac{2 5 - 5}{5 + 1}

\frac{2 5 - 5}{5 + 1}

有理化:

\frac{2 ( 5 - 1 ) 5 - 5}{4}

\frac{2 5 - 5}{5 + 1}

乘以共轭根式

\frac{5 - 1}{5 - 1}

= \frac{2 5 - 5 ( 5 - 1 )}{( 5 + 1 ) ( 5 - 1 )}

(5 + 1) (5 - 1) = 4

(5 + 1) (5 - 1)

使用平方差公式:

(a + b) (a - b) = a^{2} - b^{2}

a = 5, b = 1

= (5)^{2} - 1^{2}

化简

(5)^{2} - 1^{2} : 4

(5)^{2} - 1^{2}

使用法则

1^{a} = 1

1^{2} = 1

= (5)^{2} - 1

(5)^{2} = 5

(5)^{2}

使用根式运算法则:

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

= (5^{\frac{1}{2}})^{2}

使用指数法则:

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

= 5^{\frac{1}{2} \cdot 2}

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

\frac{1}{2} \cdot 2

分式相乘:

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

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

约分:

2

= 1

= 5

= 5 - 1

数字相减:

5 - 1 = 4

= 4

= 4

= \frac{2 ( 5 - 1 ) 5 - 5}{4}

= \frac{2 ( 5 - 1 ) 5 - 5}{4}

= \frac{2 ( 5 - 1 ) 5 - 5}{4}

= \frac{27}{10} \cdot 1 0^{- 4} \cdot \frac{49}{5} \cdot \frac{2 ( 5 - 1 ) 5 - 5}{4}

化简

\frac{27}{10} \cdot 1 0^{- 4} \cdot \frac{49}{5} \cdot \frac{2 ( 5 - 1 ) 5 - 5}{4} : \frac{1323 2 ( 5 - 1 ) 5 - 5}{2000000}

\frac{27}{10} \cdot 1 0^{- 4} \cdot \frac{49}{5} \cdot \frac{2 ( 5 - 1 ) 5 - 5}{4}

使用指数法则:

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

1 0^{- 4} = \frac{1}{1 0 ^{4}}

= \frac{49}{5} \cdot \frac{27}{10} \cdot \frac{1}{1 0 ^{4}} \cdot \frac{2 ( 5 - 1 ) 5 - 5}{4}

分式相乘:

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

= \frac{27 \cdot 1 \cdot 49 2 ( 5 - 1 ) 5 - 5}{10 \cdot 1 0 ^{4} \cdot 5 \cdot 4}

数字相乘:

27 \cdot 1 \cdot 49 = 1323

= \frac{1323 2 ( 5 - 1 ) 5 - 5}{1 0 ^{4} \cdot 10 \cdot 5 \cdot 4}

数字相乘:

10 \cdot 5 \cdot 4 = 200

= \frac{1323 2 ( 5 - 1 ) 5 - 5}{1 0 ^{4} \cdot 200}

分解

1 0^{4} : 2^{4} \cdot 5^{4}

因式分解

10 = 2 \cdot 5

= (2 \cdot 5)^{4}

使用指数法则:

(ab)^{c} = a^{c} b^{c}

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

分解

200 : 2^{3} \cdot 5^{2}

因式分解

200 = 2^{3} \cdot 5^{2}

= \frac{1323 2 ( 5 - 1 ) 5 - 5}{2 ^{4} \cdot 5 ^{4} \cdot 2 ^{3} \cdot 5 ^{2}}

2^{3} \cdot 5^{2} \cdot 2^{4} \cdot 5^{4} = 2^{7} \cdot 5^{6}

2^{3} \cdot 5^{2} \cdot 2^{4} \cdot 5^{4}

使用指数法则:

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

2^{3} \cdot 2^{4} = 2^{3 + 4}

= 5^{2} \cdot 2^{3 + 4} \cdot 5^{4}

数字相加:

3 + 4 = 7

= 5^{2} \cdot 2^{7} \cdot 5^{4}

使用指数法则:

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

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

= 2^{7} \cdot 5^{2 + 4}

数字相加:

2 + 4 = 6

= 2^{7} \cdot 5^{6}

= \frac{1323 2 ( 5 - 1 ) 5 - 5}{2 ^{7} \cdot 5 ^{6}}

消掉

\frac{1323 2 ( 5 - 1 ) 5 - 5}{2 ^{7} \cdot 5 ^{6}} : \frac{1323 ( 5 - 1 ) 5 - 5}{5 ^{6} \cdot 2 ^{\frac{13}{2}}}

\frac{1323 2 ( 5 - 1 ) 5 - 5}{2 ^{7} \cdot 5 ^{6}}

使用根式运算法则:

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

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

= \frac{1323 \cdot 2 ^{\frac{1}{2}} ( 5 - 1 ) 5 - 5}{2 ^{7} \cdot 5 ^{6}}

使用指数法则:

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

\frac{2 ^{\frac{1}{2}}}{2 ^{7}} = \frac{1}{2 ^{7 - \frac{1}{2}}}

= \frac{1323 ( 5 - 1 ) 5 - 5}{5 ^{6} \cdot 2 ^{- \frac{1}{2} + 7}}

数字相减:

7 - \frac{1}{2} = \frac{13}{2}

= \frac{1323 ( 5 - 1 ) 5 - 5}{5 ^{6} \cdot 2 ^{\frac{13}{2}}}

= \frac{1323 ( 5 - 1 ) 5 - 5}{5 ^{6} \cdot 2 ^{\frac{13}{2}}}

2^{\frac{13}{2}} = 2^{6} 2

2^{\frac{13}{2}}

2^{\frac{13}{2}} = 2^{6 + \frac{1}{2}}

= 2^{6 + \frac{1}{2}}

使用指数法则:

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

= 2^{6} \cdot 2^{\frac{1}{2}}

整理后得

= 2^{6} 2

= \frac{1323 ( 5 - 1 ) 5 - 5}{5 ^{6} \cdot 2 ^{6} 2}

5^{6} \cdot 2^{6} 2 = 10000002

5^{6} \cdot 2^{6} 2

5^{6} = 15625

= 2^{6} \cdot 156252

2^{6} = 64

= 15625 \cdot 642

数字相乘:

15625 \cdot 64 = 1000000

= 10000002

= \frac{1323 ( 5 - 1 ) 5 - 5}{1000000 2}

\frac{1323 ( 5 - 1 ) 5 - 5}{1000000 2}

有理化:

\frac{1323 2 ( 5 - 1 ) 5 - 5}{2000000}

\frac{1323 ( 5 - 1 ) 5 - 5}{1000000 2}

乘以共轭根式

\frac{2}{2}

= \frac{1323 ( 5 - 1 ) 5 - 5 2}{1000000 2 2}

100000022 = 2000000

100000022

使用根式运算法则:

a a = a

22 = 2

= 1000000 \cdot 2

数字相乘:

1000000 \cdot 2 = 2000000

= 2000000

= \frac{1323 2 ( 5 - 1 ) 5 - 5}{2000000}

= \frac{1323 2 ( 5 - 1 ) 5 - 5}{2000000}

= \frac{1323 2 ( 5 - 1 ) 5 - 5}{2000000}

流行的例子

sin^2(45)-cos^2(45)

sin^{2} (4 5^{\circ}) - cos^{2} (4 5^{\circ})

- sin (30 0^{\circ})

10 \cdot cos (5 2^{\circ})

arctan (22)

arctan (23)