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 >

(sin(15)-cos(15))/(tan(15))

解答

\frac{sin ( 1 5 ^{\circ} ) - cos ( 1 5 ^{\circ} )}{tan ( 1 5 ^{\circ} )}

解答

- \frac{2 2 + 6}{2}

+1

十进制

- 2.63895 \dots

求解步骤

\frac{sin ( 1 5 ^{\circ} ) - cos ( 1 5 ^{\circ} )}{tan ( 1 5 ^{\circ} )}

使用三角恒等式改写:

tan (1 5^{\circ}) = \frac{sin ( 1 5 ^{\circ} )}{cos ( 1 5 ^{\circ} )}

tan (1 5^{\circ})

使用基本三角恒等式:

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

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

= \frac{sin ( 1 5 ^{\circ} ) - cos ( 1 5 ^{\circ} )}{\frac{s i n ( 1 5 ^{\circ} )}{c o s ( 1 5 ^{\circ} )}}

化简

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

使用三角恒等式改写:

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

cos (1 5^{\circ})

使用三角恒等式改写:

cos (4 5^{\circ}) cos (3 0^{\circ}) + sin (4 5^{\circ}) sin (3 0^{\circ})

cos (1 5^{\circ})

将

cos (1 5^{\circ})

写为

cos (4 5^{\circ} - 3 0^{\circ})

= cos (4 5^{\circ} - 3 0^{\circ})

使用角差恒等式:

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

= cos (4 5^{\circ}) cos (3 0^{\circ}) + sin (4 5^{\circ}) sin (3 0^{\circ})

= cos (4 5^{\circ}) cos (3 0^{\circ}) + sin (4 5^{\circ}) sin (3 0^{\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:

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

cos (3 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 (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}

使用以下普通恒等式:

sin (3 0^{\circ}) = \frac{1}{2}

sin (3 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}

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

化简

\frac{2}{2} \cdot \frac{3}{2} + \frac{2}{2} \cdot \frac{1}{2} : \frac{6 + 2}{4}

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

\frac{2}{2} \cdot \frac{3}{2} = \frac{6}{4}

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

分式相乘:

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

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

数字相乘:

2 \cdot 2 = 4

= \frac{2 3}{4}

化简

23 : 6

23

使用根式运算法则:

a b = a \cdot b

23 = 2 \cdot 3

= 2 \cdot 3

数字相乘:

2 \cdot 3 = 6

= 6

= \frac{6}{4}

\frac{2}{2} \cdot \frac{1}{2} = \frac{2}{4}

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

分式相乘:

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

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

乘以:

2 \cdot 1 = 2

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

数字相乘:

2 \cdot 2 = 4

= \frac{2}{4}

= \frac{6}{4} + \frac{2}{4}

使用法则

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

= \frac{6 + 2}{4}

= \frac{6 + 2}{4}

使用三角恒等式改写:

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

sin (1 5^{\circ})

使用三角恒等式改写:

sin (4 5^{\circ}) cos (3 0^{\circ}) - cos (4 5^{\circ}) sin (3 0^{\circ})

sin (1 5^{\circ})

将

sin (1 5^{\circ})

写为

sin (4 5^{\circ} - 3 0^{\circ})

= sin (4 5^{\circ} - 3 0^{\circ})

使用角差恒等式:

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

= sin (4 5^{\circ}) cos (3 0^{\circ}) - cos (4 5^{\circ}) sin (3 0^{\circ})

= sin (4 5^{\circ}) cos (3 0^{\circ}) - cos (4 5^{\circ}) sin (3 0^{\circ})

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}

使用以下普通恒等式:

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

cos (3 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:

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 (3 0^{\circ}) = \frac{1}{2}

sin (3 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}

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

化简

\frac{2}{2} \cdot \frac{3}{2} - \frac{2}{2} \cdot \frac{1}{2} : \frac{6 - 2}{4}

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

\frac{2}{2} \cdot \frac{3}{2} = \frac{6}{4}

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

分式相乘:

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

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

数字相乘:

2 \cdot 2 = 4

= \frac{2 3}{4}

化简

23 : 6

23

使用根式运算法则:

a b = a \cdot b

23 = 2 \cdot 3

= 2 \cdot 3

数字相乘:

2 \cdot 3 = 6

= 6

= \frac{6}{4}

\frac{2}{2} \cdot \frac{1}{2} = \frac{2}{4}

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

分式相乘:

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

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

乘以:

2 \cdot 1 = 2

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

数字相乘:

2 \cdot 2 = 4

= \frac{2}{4}

= \frac{6}{4} - \frac{2}{4}

使用法则

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

= \frac{6 - 2}{4}

= \frac{6 - 2}{4}

= \frac{\frac{6 + 2}{4} \cdot \frac{6 - 2}{4} - ( \frac{6 + 2}{4} ) ^{2}}{\frac{6 - 2}{4}}

化简

\frac{\frac{6 + 2}{4} \cdot \frac{6 - 2}{4} - ( \frac{6 + 2}{4} ) ^{2}}{\frac{6 - 2}{4}} : - \frac{2 2 + 6}{2}

\frac{\frac{6 + 2}{4} \cdot \frac{6 - 2}{4} - ( \frac{6 + 2}{4} ) ^{2}}{\frac{6 - 2}{4}}

使用分式法则:

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

= \frac{( \frac{6 + 2}{4} \cdot \frac{6 - 2}{4} - ( \frac{6 + 2}{4} ) ^{2} ) \cdot 4}{6 - 2}

\frac{6 + 2}{4} \cdot \frac{6 - 2}{4} = \frac{1}{4}

\frac{6 + 2}{4} \cdot \frac{6 - 2}{4}

分式相乘:

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

= \frac{( 6 + 2 ) ( 6 - 2 )}{4 \cdot 4}

数字相乘:

4 \cdot 4 = 16

= \frac{( 6 + 2 ) ( 6 - 2 )}{16}

乘开

(6 + 2) (6 - 2) : 4

(6 + 2) (6 - 2)

使用平方差公式:

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

a = 6, b = 2

= (6)^{2} - (2)^{2}

化简

(6)^{2} - (2)^{2} : 4

(6)^{2} - (2)^{2}

(6)^{2} = 6

(6)^{2}

使用根式运算法则:

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

= (6^{\frac{1}{2}})^{2}

使用指数法则:

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

= 6^{\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

= 6

(2)^{2} = 2

(2)^{2}

使用根式运算法则:

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

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

使用指数法则:

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

= 2^{\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

= 2

= 6 - 2

数字相减:

6 - 2 = 4

= 4

= 4

= \frac{4}{16}

约分:

4

= \frac{1}{4}

(\frac{6 + 2}{4})^{2} = \frac{2 + 3}{4}

(\frac{6 + 2}{4})^{2}

使用指数法则:

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

= \frac{( 6 + 2 ) ^{2}}{4 ^{2}}

(6 + 2)^{2} = 8 + 43

(6 + 2)^{2}

使用完全平方公式:

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

a = 6, b = 2

= (6)^{2} + 262 + (2)^{2}

化简

(6)^{2} + 262 + (2)^{2} : 8 + 43

(6)^{2} + 262 + (2)^{2}

(6)^{2} = 6

(6)^{2}

使用根式运算法则:

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

= (6^{\frac{1}{2}})^{2}

使用指数法则:

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

= 6^{\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

= 6

262 = 43

262

分解整数

6 = 2 \cdot 3

= 2 2 \cdot 3 2

使用根式运算法则:

n ab = n a n b

2 \cdot 3 = 23

= 2232

使用根式运算法则:

a a = a

22 = 2

= 2 \cdot 23

数字相乘:

2 \cdot 2 = 4

= 43

(2)^{2} = 2

(2)^{2}

使用根式运算法则:

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

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

使用指数法则:

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

= 2^{\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

= 2

= 6 + 43 + 2

数字相加:

6 + 2 = 8

= 8 + 43

= 8 + 43

= \frac{8 + 4 3}{4 ^{2}}

分解

8 + 43 : 4 (2 + 3)

8 + 43

改写为

= 4 \cdot 2 + 43

因式分解出通项

4

= 4 (2 + 3)

= \frac{4 ( 2 + 3 )}{4 ^{2}}

约分:

4

= \frac{2 + 3}{4}

= \frac{4 ( \frac{1}{4} - \frac{2 + 3}{4} )}{6 - 2}

合并分式

\frac{1}{4} - \frac{2 + 3}{4} : \frac{1 - ( 2 + 3 )}{4}

使用法则

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

= \frac{1 - ( 2 + 3 )}{4}

= \frac{4 ( \frac{- ( 2 + 3 ) + 1}{4} )}{6 - 2}

去除括号:

(a) = a

= \frac{\frac{1 - ( 2 + 3 )}{4} \cdot 4}{6 - 2}

乘

\frac{1 - ( 2 + 3 )}{4} \cdot 4 : - 1 - 3

\frac{1 - ( 2 + 3 )}{4} \cdot 4

分式相乘:

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

= \frac{( 1 - ( 2 + 3 ) ) \cdot 4}{4}

约分:

4

= 1 - (2 + 3)

- (2 + 3) : - 2 - 3

- (2 + 3)

打开括号

= - (2) - (3)

使用加减运算法则

+ (- a) = - a

= - 2 - 3

= 1 - 2 - 3

数字相减:

1 - 2 = - 1

= - 1 - 3

= \frac{- 1 - 3}{6 - 2}

\frac{- 1 - 3}{6 - 2}

有理化:

- \frac{2 2 + 6}{2}

\frac{- 1 - 3}{6 - 2}

乘以共轭根式

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

= \frac{( - 1 - 3 ) ( 6 + 2 )}{( 6 - 2 ) ( 6 + 2 )}

(- 1 - 3) (6 + 2) = - 26 - 42

(- 1 - 3) (6 + 2)

使用 FOIL 方法:

(a + b) (c + d) = a c + a d + b c + b d

a = - 1, b = - 3, c = 6, d = 2

= (- 1) 6 + (- 1) 2 + (- 3) 6 + (- 3) 2

使用加减运算法则

+ (- a) = - a

= - 1 \cdot 6 - 1 \cdot 2 - 36 - 32

化简

- 1 \cdot 6 - 1 \cdot 2 - 36 - 32 : - 26 - 42

- 1 \cdot 6 - 1 \cdot 2 - 36 - 32

1 \cdot 6 = 6

1 \cdot 6

乘以:

1 \cdot 6 = 6

= 6

1 \cdot 2 = 2

1 \cdot 2

乘以:

1 \cdot 2 = 2

= 2

36 = 32

36

分解整数

6 = 3 \cdot 2

= 3 3 \cdot 2

使用根式运算法则:

n ab = n a n b

3 \cdot 2 = 32

= 332

使用根式运算法则:

a a = a

33 = 3

= 32

32 = 6

32

使用根式运算法则:

a b = a \cdot b

32 = 3 \cdot 2

= 3 \cdot 2

数字相乘:

3 \cdot 2 = 6

= 6

= - 6 - 2 - 32 - 6

同类项相加:

- 2 - 32 = - 42

= - 6 - 42 - 6

同类项相加:

- 6 - 6 = - 26

= - 26 - 42

= - 26 - 42

(6 - 2) (6 + 2) = 4

(6 - 2) (6 + 2)

使用平方差公式:

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

a = 6, b = 2

= (6)^{2} - (2)^{2}

化简

(6)^{2} - (2)^{2} : 4

(6)^{2} - (2)^{2}

(6)^{2} = 6

(6)^{2}

使用根式运算法则:

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

= (6^{\frac{1}{2}})^{2}

使用指数法则:

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

= 6^{\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

= 6

(2)^{2} = 2

(2)^{2}

使用根式运算法则:

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

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

使用指数法则:

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

= 2^{\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

= 2

= 6 - 2

数字相减:

6 - 2 = 4

= 4

= 4

= \frac{- 2 6 - 4 2}{4}

分解

- 26 - 42 : - 2 (6 + 22)

- 26 - 42

改写为

= - 26 - 2 \cdot 22

因式分解出通项

2

= - 2 (6 + 22)

= - \frac{2 ( 6 + 2 2 )}{4}

约分:

2

= - \frac{2 2 + 6}{2}

= - \frac{2 2 + 6}{2}

= - \frac{2 2 + 6}{2}

流行的例子

10 cos (3 7^{\circ})

arcsin((3.9)/(8.1))

arcsin (\frac{3.9}{8.1})

arcsin (\frac{8}{13})

- sin (4 π)

(sin(3*0.1))/(0.1)

\frac{sin ( 3 \cdot 0.1 )}{0.1}