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受欢迎的三角函数 >

sin(x)+sin(90-x)=sin(90)

解答

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

解答

x = 9 0^{\circ} + 36 0^{\circ} n, x = 36 0^{\circ} + 36 0^{\circ} n

+1

弧度

x = \frac{π}{2} + 2 πn, x = 2 π + 2 πn

求解步骤

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

sin (9 0^{\circ}) = 1

sin (9 0^{\circ})

使用以下普通恒等式:

sin (9 0^{\circ}) = 1

sin (9 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}

= 1

= 1

sin (x) + sin (9 0^{\circ} - x) = 1

使用三角恒等式改写

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

使用和差化积恒等式:

sin (s) + sin (t) = 2 sin (\frac{s + t}{2}) cos (\frac{s - t}{2})

= 2 sin (\frac{x + 9 0 ^{\circ} - x}{2}) cos (\frac{x - ( 9 0 ^{\circ} - x )}{2})

化简

2 sin (\frac{x + 9 0 ^{\circ} - x}{2}) cos (\frac{x - ( 9 0 ^{\circ} - x )}{2}) : 2 cos (\frac{4 x - 18 0 ^{\circ}}{4})

2 sin (\frac{x + 9 0 ^{\circ} - x}{2}) cos (\frac{x - ( 9 0 ^{\circ} - x )}{2})

\frac{x + 9 0 ^{\circ} - x}{2} = 4 5^{\circ}

\frac{x + 9 0 ^{\circ} - x}{2}

x + 9 0^{\circ} - x = 9 0^{\circ}

x + 9 0^{\circ} - x

对同类项分组

= x - x + 9 0^{\circ}

同类项相加:

x - x = 0

= 9 0^{\circ}

= \frac{9 0 ^{\circ}}{2}

使用分式法则:

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

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

数字相乘:

2 \cdot 2 = 4

= 4 5^{\circ}

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

\frac{x - ( 9 0 ^{\circ} - x )}{2} = \frac{4 x - 18 0 ^{\circ}}{4}

\frac{x - ( 9 0 ^{\circ} - x )}{2}

乘开

x - (9 0^{\circ} - x) : 2 x - 9 0^{\circ}

x - (9 0^{\circ} - x)

- (9 0^{\circ} - x) : - 9 0^{\circ} + x

- (9 0^{\circ} - x)

打开括号

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

使用加减运算法则

- (- a) = a, - (a) = - a

= - 9 0^{\circ} + x

= x - 9 0^{\circ} + x

化简

x - 9 0^{\circ} + x : 2 x - 9 0^{\circ}

x - 9 0^{\circ} + x

对同类项分组

= x + x - 9 0^{\circ}

同类项相加:

x + x = 2 x

= 2 x - 9 0^{\circ}

= 2 x - 9 0^{\circ}

= \frac{2 x - 9 0 ^{\circ}}{2}

化简

2 x - 9 0^{\circ} : \frac{4 x - 18 0 ^{\circ}}{2}

2 x - 9 0^{\circ}

将项转换为分式:

2 x = \frac{2 x 2}{2}

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

数字相乘:

2 \cdot 2 = 4

= \frac{4 x - 18 0 ^{\circ}}{2}

= \frac{\frac{4 x - 18 0 ^{\circ}}{2}}{2}

使用分式法则:

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

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

数字相乘:

2 \cdot 2 = 4

= \frac{4 x - 18 0 ^{\circ}}{4}

= 2 sin (4 5^{\circ}) cos (\frac{4 x - 18 0 ^{\circ}}{4})

化简

sin (4 5^{\circ}) : \frac{2}{2}

sin (4 5^{\circ})

使用以下普通恒等式:

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

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}

= 2 \cdot \frac{2}{2} cos (\frac{4 x - 18 0 ^{\circ}}{4})

分式相乘:

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

= \frac{2 \cdot 2 cos ( \frac{4 x - 18 0 ^{\circ}}{4} )}{2}

约分:

2

= 2 cos (\frac{4 x - 18 0 ^{\circ}}{4})

= 2 cos (\frac{4 x - 18 0 ^{\circ}}{4})

2 cos (\frac{4 x - 18 0 ^{\circ}}{4}) = 1

两边除以

2

2 cos (\frac{4 x - 18 0 ^{\circ}}{4}) = 1

两边除以

2

\frac{2 cos ( \frac{4 x - 18 0 ^{\circ}}{4} )}{2} = \frac{1}{2}

化简

\frac{2 cos ( \frac{4 x - 18 0 ^{\circ}}{4} )}{2} = \frac{1}{2}

化简

\frac{2 cos ( \frac{4 x - 18 0 ^{\circ}}{4} )}{2} : cos (\frac{4 x - 18 0 ^{\circ}}{4})

\frac{2 cos ( \frac{4 x - 18 0 ^{\circ}}{4} )}{2}

约分:

2

= cos (\frac{4 x - 18 0 ^{\circ}}{4})

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}

cos (\frac{4 x - 18 0 ^{\circ}}{4}) = \frac{2}{2}

cos (\frac{4 x - 18 0 ^{\circ}}{4}) = \frac{2}{2}

cos (\frac{4 x - 18 0 ^{\circ}}{4}) = \frac{2}{2}

cos (\frac{4 x - 18 0 ^{\circ}}{4}) = \frac{2}{2}

的通解

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{4 x - 18 0 ^{\circ}}{4} = 4 5^{\circ} + 36 0^{\circ} n, \frac{4 x - 18 0 ^{\circ}}{4} = 31 5^{\circ} + 36 0^{\circ} n

\frac{4 x - 18 0 ^{\circ}}{4} = 4 5^{\circ} + 36 0^{\circ} n, \frac{4 x - 18 0 ^{\circ}}{4} = 31 5^{\circ} + 36 0^{\circ} n

解

\frac{4 x - 18 0 ^{\circ}}{4} = 4 5^{\circ} + 36 0^{\circ} n : x = 9 0^{\circ} + 36 0^{\circ} n

\frac{4 x - 18 0 ^{\circ}}{4} = 4 5^{\circ} + 36 0^{\circ} n

在两边乘以

4

\frac{4 x - 18 0 ^{\circ}}{4} = 4 5^{\circ} + 36 0^{\circ} n

在两边乘以

4

\frac{4 ( 4 x - 18 0 ^{\circ} )}{4} = 4 \cdot 4 5^{\circ} + 4 \cdot 36 0^{\circ} n

化简

\frac{4 ( 4 x - 18 0 ^{\circ} )}{4} = 4 \cdot 4 5^{\circ} + 4 \cdot 36 0^{\circ} n

化简

\frac{4 ( 4 x - 18 0 ^{\circ} )}{4} : 4 x - 18 0^{\circ}

\frac{4 ( 4 x - 18 0 ^{\circ} )}{4}

数字相除:

\frac{4}{4} = 1

= 4 x - 18 0^{\circ}

化简

4 \cdot 4 5^{\circ} + 4 \cdot 36 0^{\circ} n : 18 0^{\circ} + 144 0^{\circ} n

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

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

4 \cdot 4 5^{\circ}

分式相乘:

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

= 18 0^{\circ}

约分:

4

= 18 0^{\circ}

4 \cdot 36 0^{\circ} n = 144 0^{\circ} n

4 \cdot 36 0^{\circ} n

数字相乘:

4 \cdot 2 = 8

= 144 0^{\circ} n

= 18 0^{\circ} + 144 0^{\circ} n

4 x - 18 0^{\circ} = 18 0^{\circ} + 144 0^{\circ} n

4 x - 18 0^{\circ} = 18 0^{\circ} + 144 0^{\circ} n

4 x - 18 0^{\circ} = 18 0^{\circ} + 144 0^{\circ} n

将

18 0^{\circ}

到右边

4 x - 18 0^{\circ} = 18 0^{\circ} + 144 0^{\circ} n

两边加上

18 0^{\circ}

4 x - 18 0^{\circ} + 18 0^{\circ} = 18 0^{\circ} + 144 0^{\circ} n + 18 0^{\circ}

化简

4 x = 36 0^{\circ} + 144 0^{\circ} n

4 x = 36 0^{\circ} + 144 0^{\circ} n

两边除以

4

4 x = 36 0^{\circ} + 144 0^{\circ} n

两边除以

4

\frac{4 x}{4} = 9 0^{\circ} + \frac{144 0 ^{\circ} n}{4}

化简

\frac{4 x}{4} = 9 0^{\circ} + \frac{144 0 ^{\circ} n}{4}

化简

\frac{4 x}{4} : x

\frac{4 x}{4}

数字相除:

\frac{4}{4} = 1

= x

化简

9 0^{\circ} + \frac{144 0 ^{\circ} n}{4} : 9 0^{\circ} + 36 0^{\circ} n

9 0^{\circ} + \frac{144 0 ^{\circ} n}{4}

消掉

9 0^{\circ} : 9 0^{\circ}

9 0^{\circ}

约分:

2

= 9 0^{\circ}

= 9 0^{\circ} + \frac{144 0 ^{\circ} n}{4}

数字相除:

\frac{8}{4} = 2

= 9 0^{\circ} + 36 0^{\circ} n

x = 9 0^{\circ} + 36 0^{\circ} n

x = 9 0^{\circ} + 36 0^{\circ} n

x = 9 0^{\circ} + 36 0^{\circ} n

解

\frac{4 x - 18 0 ^{\circ}}{4} = 31 5^{\circ} + 36 0^{\circ} n : x = 36 0^{\circ} + 36 0^{\circ} n

\frac{4 x - 18 0 ^{\circ}}{4} = 31 5^{\circ} + 36 0^{\circ} n

在两边乘以

4

\frac{4 x - 18 0 ^{\circ}}{4} = 31 5^{\circ} + 36 0^{\circ} n

在两边乘以

4

\frac{4 ( 4 x - 18 0 ^{\circ} )}{4} = 4 \cdot 31 5^{\circ} + 4 \cdot 36 0^{\circ} n

化简

\frac{4 ( 4 x - 18 0 ^{\circ} )}{4} = 4 \cdot 31 5^{\circ} + 4 \cdot 36 0^{\circ} n

化简

\frac{4 ( 4 x - 18 0 ^{\circ} )}{4} : 4 x - 18 0^{\circ}

\frac{4 ( 4 x - 18 0 ^{\circ} )}{4}

数字相除:

\frac{4}{4} = 1

= 4 x - 18 0^{\circ}

化简

4 \cdot 31 5^{\circ} + 4 \cdot 36 0^{\circ} n : 126 0^{\circ} + 144 0^{\circ} n

4 \cdot 31 5^{\circ} + 4 \cdot 36 0^{\circ} n

4 \cdot 31 5^{\circ} = 126 0^{\circ}

4 \cdot 31 5^{\circ}

分式相乘:

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

= 126 0^{\circ}

约分:

4

= 126 0^{\circ}

4 \cdot 36 0^{\circ} n = 144 0^{\circ} n

4 \cdot 36 0^{\circ} n

数字相乘:

4 \cdot 2 = 8

= 144 0^{\circ} n

= 126 0^{\circ} + 144 0^{\circ} n

4 x - 18 0^{\circ} = 126 0^{\circ} + 144 0^{\circ} n

4 x - 18 0^{\circ} = 126 0^{\circ} + 144 0^{\circ} n

4 x - 18 0^{\circ} = 126 0^{\circ} + 144 0^{\circ} n

将

18 0^{\circ}

到右边

4 x - 18 0^{\circ} = 126 0^{\circ} + 144 0^{\circ} n

两边加上

18 0^{\circ}

4 x - 18 0^{\circ} + 18 0^{\circ} = 126 0^{\circ} + 144 0^{\circ} n + 18 0^{\circ}

化简

4 x = 144 0^{\circ} + 144 0^{\circ} n

4 x = 144 0^{\circ} + 144 0^{\circ} n

两边除以

4

4 x = 144 0^{\circ} + 144 0^{\circ} n

两边除以

4

\frac{4 x}{4} = 36 0^{\circ} + \frac{144 0 ^{\circ} n}{4}

化简

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

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

x = 9 0^{\circ} + 36 0^{\circ} n, x = 36 0^{\circ} + 36 0^{\circ} n

作图

流行的例子

sin(2x)=cos(x-60)

sin (2 x) = cos (x - 6 0^{\circ})

tan(x)= 1/(cos^2(x))

tan (x) = \frac{1}{cos ^{2} ( x )}

2csc(θ)=sqrt(2)cot(θ)+3csc(θ)

2 csc (θ) = 2 cot (θ) + 3 csc (θ)

arctan (x) = 180

cos(θ)=(2sqrt(2))/3

cos (θ) = \frac{2 2}{3}