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受欢迎的三角函数 >

cos(x)=cos(x-c)

解答

cos (x) = cos (x - c)

解答

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

求解步骤

cos (x) = cos (x - c)

两边减去

cos (x - c)

cos (x) - cos (x - c) = 0

使用三角恒等式改写

cos (x) - cos (x - c)

使用和差化积恒等式:

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

= - 2 sin (\frac{x + x - c}{2}) sin (\frac{x - ( x - c )}{2})

化简

- 2 sin (\frac{x + x - c}{2}) sin (\frac{x - ( x - c )}{2}) : - 2 sin (\frac{c}{2}) sin (\frac{2 x - c}{2})

- 2 sin (\frac{x + x - c}{2}) sin (\frac{x - ( x - c )}{2})

同类项相加:

x + x = 2 x

= - 2 sin (\frac{2 x - c}{2}) sin (\frac{x - ( x - c )}{2})

乘开

x - (x - c) : c

x - (x - c)

- (x - c) : - x + c

- (x - c)

打开括号

= - (x) - (- c)

使用加减运算法则

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

= - x + c

= x - x + c

同类项相加:

x - x = 0

= c

= - 2 sin (\frac{c}{2}) sin (\frac{2 x - c}{2})

= - 2 sin (\frac{c}{2}) sin (\frac{2 x - c}{2})

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

使用零因数法则： If

ab = 0

then

a = 0

or

b = 0

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

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

的通解

sin (x)

周期表（周期为

2 πn

"）：

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} sin (x) 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2}

\frac{2 x - c}{2} = 0 + 2 πn, \frac{2 x - c}{2} = π + 2 πn

\frac{2 x - c}{2} = 0 + 2 πn, \frac{2 x - c}{2} = π + 2 πn

解

\frac{2 x - c}{2} = 0 + 2 πn : x = 2 πn + \frac{c}{2}

\frac{2 x - c}{2} = 0 + 2 πn

0 + 2 πn = 2 πn

\frac{2 x - c}{2} = 2 πn

在两边乘以

2

\frac{2 x - c}{2} = 2 πn

在两边乘以

2

\frac{2 ( 2 x - c )}{2} = 2 \cdot 2 πn

化简

2 x - c = 4 πn

2 x - c = 4 πn

将

c

到右边

2 x - c = 4 πn

两边加上

c

2 x - c + c = 4 πn + c

化简

2 x = 4 πn + c

2 x = 4 πn + c

两边除以

2

2 x = 4 πn + c

两边除以

2

\frac{2 x}{2} = \frac{4 πn}{2} + \frac{c}{2}

化简

x = 2 πn + \frac{c}{2}

x = 2 πn + \frac{c}{2}

解

\frac{2 x - c}{2} = π + 2 πn : x = π + 2 πn + \frac{c}{2}

\frac{2 x - c}{2} = π + 2 πn

在两边乘以

2

\frac{2 x - c}{2} = π + 2 πn

在两边乘以

2

\frac{2 ( 2 x - c )}{2} = 2 π + 2 \cdot 2 πn

化简

2 x - c = 2 π + 4 πn

2 x - c = 2 π + 4 πn

将

c

到右边

2 x - c = 2 π + 4 πn

两边加上

c

2 x - c + c = 2 π + 4 πn + c

化简

2 x = 2 π + 4 πn + c

2 x = 2 π + 4 πn + c

两边除以

2

2 x = 2 π + 4 πn + c

两边除以

2

\frac{2 x}{2} = \frac{2 π}{2} + \frac{4 πn}{2} + \frac{c}{2}

化简

\frac{2 x}{2} = \frac{2 π}{2} + \frac{4 πn}{2} + \frac{c}{2}

化简

\frac{2 x}{2} : x

\frac{2 x}{2}

数字相除:

\frac{2}{2} = 1

= x

化简

\frac{2 π}{2} + \frac{4 πn}{2} + \frac{c}{2} : π + 2 πn + \frac{c}{2}

\frac{2 π}{2} + \frac{4 πn}{2} + \frac{c}{2}

数字相除:

\frac{2}{2} = 1

= π + \frac{4 πn}{2} + \frac{c}{2}

数字相除:

\frac{4}{2} = 2

= π + 2 πn + \frac{c}{2}

x = π + 2 πn + \frac{c}{2}

x = π + 2 πn + \frac{c}{2}

x = π + 2 πn + \frac{c}{2}

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

作图

流行的例子

-2sqrt(2)cos(θ)=2

- 22 cos (θ) = 2

cos(θ)=(sqrt(6))/2

cos (θ) = \frac{6}{2}

5 sin (60 t) = 0

sin(2θ)=0.4905

sin (2 θ) = 0.4905

tan(θ)=(-4.86)/(14.56)

tan (θ) = \frac{- 4.86}{14.56}