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受欢迎的三角函数 >

sin(x-20)= 1/(sqrt(2))

解答

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

解答

x = 36 0^{\circ} n + 6 5^{\circ}, x = 36 0^{\circ} n + 15 5^{\circ}

+1

弧度

x = \frac{13 π}{36} + 2 πn, x = \frac{31 π}{36} + 2 πn

求解步骤

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

化简

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

\frac{1}{2}

乘以共轭根式

\frac{2}{2}

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

1 \cdot 2 = 2

22 = 2

22

使用根式运算法则:

a a = a

22 = 2

= 2

= \frac{2}{2}

sin (x - 2 0^{\circ}) = \frac{2}{2}

sin (x - 2 0^{\circ}) = \frac{2}{2}

的通解

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}

x - 2 0^{\circ} = 4 5^{\circ} + 36 0^{\circ} n, x - 2 0^{\circ} = 13 5^{\circ} + 36 0^{\circ} n

x - 2 0^{\circ} = 4 5^{\circ} + 36 0^{\circ} n, x - 2 0^{\circ} = 13 5^{\circ} + 36 0^{\circ} n

解

x - 2 0^{\circ} = 4 5^{\circ} + 36 0^{\circ} n : x = 36 0^{\circ} n + 6 5^{\circ}

x - 2 0^{\circ} = 4 5^{\circ} + 36 0^{\circ} n

将

2 0^{\circ}

到右边

x - 2 0^{\circ} = 4 5^{\circ} + 36 0^{\circ} n

两边加上

2 0^{\circ}

x - 2 0^{\circ} + 2 0^{\circ} = 4 5^{\circ} + 36 0^{\circ} n + 2 0^{\circ}

化简

x - 2 0^{\circ} + 2 0^{\circ} = 4 5^{\circ} + 36 0^{\circ} n + 2 0^{\circ}

化简

x - 2 0^{\circ} + 2 0^{\circ} : x

x - 2 0^{\circ} + 2 0^{\circ}

同类项相加:

- 2 0^{\circ} + 2 0^{\circ} = 0

= x

化简

4 5^{\circ} + 36 0^{\circ} n + 2 0^{\circ} : 36 0^{\circ} n + 6 5^{\circ}

4 5^{\circ} + 36 0^{\circ} n + 2 0^{\circ}

对同类项分组

= 36 0^{\circ} n + 4 5^{\circ} + 2 0^{\circ}

4, 9

的最小公倍数:

36

4, 9

最小公倍数 (LCM)

4

质因数分解:

2 \cdot 2

4

4

除以

24 = 2 \cdot 2

= 2 \cdot 2

9

质因数分解:

3 \cdot 3

9

9

除以

39 = 3 \cdot 3

= 3 \cdot 3

将每个因子乘以它在

4

或

9

中出现的最多次数

= 2 \cdot 2 \cdot 3 \cdot 3

数字相乘:

2 \cdot 2 \cdot 3 \cdot 3 = 36

= 36

根据最小公倍数调整分式

将每个分子乘以其分母转变为最小公倍数所要乘以的同一数值

36

对于

4 5^{\circ} :

将分母和分子乘以

9

4 5^{\circ} = \frac{18 0 ^{\circ} 9}{4 \cdot 9} = 4 5^{\circ}

对于

2 0^{\circ} :

将分母和分子乘以

4

2 0^{\circ} = \frac{18 0 ^{\circ} 4}{9 \cdot 4} = 2 0^{\circ}

= 4 5^{\circ} + 2 0^{\circ}

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{18 0 ^{\circ} 9 + 18 0 ^{\circ} 4}{36}

同类项相加:

162 0^{\circ} + 72 0^{\circ} = 234 0^{\circ}

= 36 0^{\circ} n + 6 5^{\circ}

x = 36 0^{\circ} n + 6 5^{\circ}

x = 36 0^{\circ} n + 6 5^{\circ}

x = 36 0^{\circ} n + 6 5^{\circ}

解

x - 2 0^{\circ} = 13 5^{\circ} + 36 0^{\circ} n : x = 36 0^{\circ} n + 15 5^{\circ}

x - 2 0^{\circ} = 13 5^{\circ} + 36 0^{\circ} n

将

2 0^{\circ}

到右边

x - 2 0^{\circ} = 13 5^{\circ} + 36 0^{\circ} n

两边加上

2 0^{\circ}

x - 2 0^{\circ} + 2 0^{\circ} = 13 5^{\circ} + 36 0^{\circ} n + 2 0^{\circ}

化简

x - 2 0^{\circ} + 2 0^{\circ} = 13 5^{\circ} + 36 0^{\circ} n + 2 0^{\circ}

化简

x - 2 0^{\circ} + 2 0^{\circ} : x

x - 2 0^{\circ} + 2 0^{\circ}

同类项相加:

- 2 0^{\circ} + 2 0^{\circ} = 0

= x

化简

13 5^{\circ} + 36 0^{\circ} n + 2 0^{\circ} : 36 0^{\circ} n + 15 5^{\circ}

13 5^{\circ} + 36 0^{\circ} n + 2 0^{\circ}

对同类项分组

= 36 0^{\circ} n + 2 0^{\circ} + 13 5^{\circ}

9, 4

的最小公倍数:

36

9, 4

最小公倍数 (LCM)

9

质因数分解:

3 \cdot 3

9

9

除以

39 = 3 \cdot 3

= 3 \cdot 3

4

质因数分解:

2 \cdot 2

4

4

除以

24 = 2 \cdot 2

= 2 \cdot 2

将每个因子乘以它在

9

或

4

中出现的最多次数

= 3 \cdot 3 \cdot 2 \cdot 2

数字相乘:

3 \cdot 3 \cdot 2 \cdot 2 = 36

= 36

根据最小公倍数调整分式

将每个分子乘以其分母转变为最小公倍数所要乘以的同一数值

36

对于

2 0^{\circ} :

将分母和分子乘以

4

2 0^{\circ} = \frac{18 0 ^{\circ} 4}{9 \cdot 4} = 2 0^{\circ}

对于

13 5^{\circ} :

将分母和分子乘以

9

13 5^{\circ} = \frac{54 0 ^{\circ} 9}{4 \cdot 9} = 13 5^{\circ}

= 2 0^{\circ} + 13 5^{\circ}

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{18 0 ^{\circ} 4 + 486 0 ^{\circ}}{36}

同类项相加:

72 0^{\circ} + 486 0^{\circ} = 558 0^{\circ}

= 36 0^{\circ} n + 15 5^{\circ}

x = 36 0^{\circ} n + 15 5^{\circ}

x = 36 0^{\circ} n + 15 5^{\circ}

x = 36 0^{\circ} n + 15 5^{\circ}

x = 36 0^{\circ} n + 6 5^{\circ}, x = 36 0^{\circ} n + 15 5^{\circ}

作图

流行的例子

cos(5x)-cos(x)=sin(5x)-sin(x)

cos (5 x) - cos (x) = sin (5 x) - sin (x)

sin(θ)= 8/17 ,cos(θ)= 15/17 ,tan(θ)

sin (θ) = \frac{8}{17}, cos (θ) = \frac{15}{17}, tan (θ)

tan (x) = \frac{7}{10}

cos(5x)+cos(x)=2cos(2x)

cos (5 x) + cos (x) = 2 cos (2 x)

cos (x) = \frac{22}{24}