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受欢迎的三角函数 >

cos(x+3)=cos(x)

解答

cos (x + 3) = cos (x)

解答

x = 2 πn - \frac{3}{2}, x = - \frac{3}{2} + π + 2 πn

+1

度数

x = - 85.94366 \dots^{\circ} + 36 0^{\circ} n, x = 94.05633 \dots^{\circ} + 36 0^{\circ} n

求解步骤

cos (x + 3) = cos (x)

两边减去

cos (x)

cos (x + 3) - cos (x) = 0

使用三角恒等式改写

cos (x + 3) - cos (x)

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 + 3 + x}{2}) sin (\frac{x + 3 - x}{2})

化简

- 2 sin (\frac{x + 3 + x}{2}) sin (\frac{x + 3 - x}{2}) : - 2 sin (\frac{3}{2}) sin (\frac{2 x + 3}{2})

- 2 sin (\frac{x + 3 + x}{2}) sin (\frac{x + 3 - x}{2})

x + 3 + x = 2 x + 3

x + 3 + x

对同类项分组

= x + x + 3

同类项相加:

x + x = 2 x

= 2 x + 3

= - 2 sin (\frac{2 x + 3}{2}) sin (\frac{x - x + 3}{2})

x + 3 - x = 3

x + 3 - x

对同类项分组

= x - x + 3

同类项相加:

x - x = 0

= 3

= - 2 sin (\frac{3}{2}) sin (\frac{2 x + 3}{2})

= - 2 sin (\frac{3}{2}) sin (\frac{2 x + 3}{2})

- 2 sin (\frac{3}{2}) sin (\frac{2 x + 3}{2}) = 0

两边除以

- 2 sin (\frac{3}{2})

- 2 sin (\frac{3}{2}) sin (\frac{2 x + 3}{2}) = 0

两边除以

- 2 sin (\frac{3}{2})

\frac{- 2 sin ( \frac{3}{2} ) sin ( \frac{2 x + 3}{2} )}{- 2 sin ( \frac{3}{2} )} = \frac{0}{- 2 sin ( \frac{3}{2} )}

化简

sin (\frac{2 x + 3}{2}) = 0

sin (\frac{2 x + 3}{2}) = 0

sin (\frac{2 x + 3}{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 + 3}{2} = 0 + 2 πn, \frac{2 x + 3}{2} = π + 2 πn

\frac{2 x + 3}{2} = 0 + 2 πn, \frac{2 x + 3}{2} = π + 2 πn

解

\frac{2 x + 3}{2} = 0 + 2 πn : x = 2 πn - \frac{3}{2}

\frac{2 x + 3}{2} = 0 + 2 πn

0 + 2 πn = 2 πn

\frac{2 x + 3}{2} = 2 πn

在两边乘以

2

\frac{2 x + 3}{2} = 2 πn

在两边乘以

2

\frac{2 ( 2 x + 3 )}{2} = 2 \cdot 2 πn

化简

2 x + 3 = 4 πn

2 x + 3 = 4 πn

将

3

到右边

2 x + 3 = 4 πn

两边减去

3

2 x + 3 - 3 = 4 πn - 3

化简

2 x = 4 πn - 3

2 x = 4 πn - 3

两边除以

2

2 x = 4 πn - 3

两边除以

2

\frac{2 x}{2} = \frac{4 πn}{2} - \frac{3}{2}

化简

x = 2 πn - \frac{3}{2}

x = 2 πn - \frac{3}{2}

解

\frac{2 x + 3}{2} = π + 2 πn : x = - \frac{3}{2} + π + 2 πn

\frac{2 x + 3}{2} = π + 2 πn

在两边乘以

2

\frac{2 x + 3}{2} = π + 2 πn

在两边乘以

2

\frac{2 ( 2 x + 3 )}{2} = 2 π + 2 \cdot 2 πn

化简

2 x + 3 = 2 π + 4 πn

2 x + 3 = 2 π + 4 πn

将

3

到右边

2 x + 3 = 2 π + 4 πn

两边减去

3

2 x + 3 - 3 = 2 π + 4 πn - 3

化简

2 x = 2 π + 4 πn - 3

2 x = 2 π + 4 πn - 3

两边除以

2

2 x = 2 π + 4 πn - 3

两边除以

2

\frac{2 x}{2} = \frac{2 π}{2} + \frac{4 πn}{2} - \frac{3}{2}

化简

\frac{2 x}{2} = \frac{2 π}{2} + \frac{4 πn}{2} - \frac{3}{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{3}{2} : - \frac{3}{2} + π + 2 πn

\frac{2 π}{2} + \frac{4 πn}{2} - \frac{3}{2}

对同类项分组

= - \frac{3}{2} + \frac{2 π}{2} + \frac{4 πn}{2}

数字相除:

\frac{2}{2} = 1

= - \frac{3}{2} + π + \frac{4 πn}{2}

数字相除:

\frac{4}{2} = 2

= - \frac{3}{2} + π + 2 πn

x = - \frac{3}{2} + π + 2 πn

x = - \frac{3}{2} + π + 2 πn

x = - \frac{3}{2} + π + 2 πn

x = 2 πn - \frac{3}{2}, x = - \frac{3}{2} + π + 2 πn

作图

流行的例子

sin(x)-cos(x)= 1/3 ,sin(2x)

sin (x) - cos (x) = \frac{1}{3}, sin (2 x)

sqrt(-9cos(θ))=(3sqrt(2))/2

- 9 cos (θ) = \frac{3 2}{2}

sec(a)=1+tan(a)

sec (a) = 1 + tan (a)

arctan(θ)= 2/(2sqrt(3))

arctan (θ) = \frac{2}{2 3}

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3 sin (x) = + sin (x)