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受欢迎的三角函数 >

sin(75)sin(45)

解答

sin (7 5^{\circ}) sin (4 5^{\circ})

解答

\frac{3 + 1}{4}

+1

十进制

0.68301 \dots

求解步骤

sin (7 5^{\circ}) sin (4 5^{\circ})

使用三角恒等式改写:

sin (7 5^{\circ}) = \frac{6 + 2}{4}

sin (7 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 (7 5^{\circ})

将

sin (7 5^{\circ})

写为

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

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

使用角和恒等式:

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}

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

化简

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

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

分式相乘:

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

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

数字相乘:

4 \cdot 2 = 8

= \frac{2 ( 6 + 2 )}{8}

分解

8 : 2^{3}

因式分解

8 = 2^{3}

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

消掉

\frac{( 6 + 2 ) 2}{2 ^{3}} : \frac{6 + 2}{2 ^{\frac{5}{2}}}

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

使用根式运算法则:

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

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

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

使用指数法则:

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

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

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

数字相减:

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

= \frac{6 + 2}{2 ^{\frac{5}{2}}}

= \frac{6 + 2}{2 ^{\frac{5}{2}}}

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

2^{\frac{5}{2}}

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

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

使用指数法则:

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

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

整理后得

= 2^{2} 2

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

2^{2} = 4

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

\frac{6 + 2}{4 2}

有理化:

\frac{1 + 3}{4}

\frac{6 + 2}{4 2}

乘以共轭根式

\frac{2}{2}

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

(6 + 2) 2 = 23 + 2

(6 + 2) 2

= 2 (6 + 2)

使用分配律:

a (b + c) = ab + a c

a = 2, b = 6, c = 2

= 26 + 22

化简

26 + 22 : 23 + 2

26 + 22

26 = 23

26

分解整数

6 = 2 \cdot 3

= 2 2 \cdot 3

使用根式运算法则:

n ab = n a n b

2 \cdot 3 = 23

= 223

使用根式运算法则:

a a = a

22 = 2

= 23

22 = 2

22

使用根式运算法则:

a a = a

22 = 2

= 2

= 23 + 2

= 23 + 2

422 = 8

422

使用根式运算法则:

a a = a

22 = 2

= 4 \cdot 2

数字相乘:

4 \cdot 2 = 8

= 8

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

分解

23 + 2 : 2 (3 + 1)

23 + 2

改写为

= 23 + 2 \cdot 1

因式分解出通项

2

= 2 (3 + 1)

= \frac{2 ( 3 + 1 )}{8}

约分:

2

= \frac{3 + 1}{4}

= \frac{3 + 1}{4}

= \frac{3 + 1}{4}

流行的例子

\frac{2}{tan ( 2 5 ^{\circ} )}

\frac{cos ^{2} ( 0 )}{2}

arcsin((3*0.54*10^{-6})/(1/200000))

arcsin (\frac{3 \cdot 0.54 \cdot 1 0 ^{- 6}}{\frac{1}{200000}})

(sec(37)+tan(37))/(sec(16)+tan(16))

\frac{sec ( 3 7 ^{\circ} ) + tan ( 3 7 ^{\circ} )}{sec ( 1 6 ^{\circ} ) + tan ( 1 6 ^{\circ} )}

- sin (- \frac{5 π}{3})