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受欢迎的三角函数 >

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

解答

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

解答

x = \frac{1}{4} + πn, x = π - \frac{1}{4} + πn

+1

度数

x = 14.32394 \dots^{\circ} + 18 0^{\circ} n, x = 165.67605 \dots^{\circ} + 18 0^{\circ} n

求解步骤

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

使用反三角函数性质

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

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

的通解

cos (x) = a \Rightarrow x = arccos (a) + 2 πn, x = 2 π - arccos (a) + 2 πn

2 x = arccos (cos (\frac{1}{2})) + 2 πn, 2 x = 2 π - arccos (cos (\frac{1}{2})) + 2 πn

2 x = arccos (cos (\frac{1}{2})) + 2 πn, 2 x = 2 π - arccos (cos (\frac{1}{2})) + 2 πn

解

2 x = arccos (cos (\frac{1}{2})) + 2 πn : x = \frac{1}{4} + πn

2 x = arccos (cos (\frac{1}{2})) + 2 πn

两边除以

2

2 x = arccos (cos (\frac{1}{2})) + 2 πn

两边除以

2

\frac{2 x}{2} = \frac{arccos ( cos ( \frac{1}{2} ) )}{2} + \frac{2 πn}{2}

化简

\frac{2 x}{2} = \frac{arccos ( cos ( \frac{1}{2} ) )}{2} + \frac{2 πn}{2}

化简

\frac{2 x}{2} : x

\frac{2 x}{2}

数字相除:

\frac{2}{2} = 1

= x

化简

\frac{arccos ( cos ( \frac{1}{2} ) )}{2} + \frac{2 πn}{2} : \frac{1}{4} + πn

\frac{arccos ( cos ( \frac{1}{2} ) )}{2} + \frac{2 πn}{2}

\frac{arccos ( cos ( \frac{1}{2} ) )}{2} = \frac{1}{4}

\frac{arccos ( cos ( \frac{1}{2} ) )}{2}

arccos (cos (\frac{1}{2})) = \frac{1}{2}

arccos (cos (\frac{1}{2}))

对于

0 \leq x \leq π, a rccos (cos (x)) = x

0 \leq \frac{1}{2} \leq π

= \frac{1}{2}

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

使用分式法则:

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

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

数字相乘:

2 \cdot 2 = 4

= \frac{1}{4}

= \frac{1}{4} + \frac{2 πn}{2}

\frac{2 πn}{2} = πn

\frac{2 πn}{2}

数字相除:

\frac{2}{2} = 1

= πn

= \frac{1}{4} + πn

x = \frac{1}{4} + πn

x = \frac{1}{4} + πn

x = \frac{1}{4} + πn

解

2 x = 2 π - arccos (cos (\frac{1}{2})) + 2 πn : x = π - \frac{1}{4} + πn

2 x = 2 π - arccos (cos (\frac{1}{2})) + 2 πn

两边除以

2

2 x = 2 π - arccos (cos (\frac{1}{2})) + 2 πn

两边除以

2

\frac{2 x}{2} = \frac{2 π}{2} - \frac{arccos ( cos ( \frac{1}{2} ) )}{2} + \frac{2 πn}{2}

化简

\frac{2 x}{2} = \frac{2 π}{2} - \frac{arccos ( cos ( \frac{1}{2} ) )}{2} + \frac{2 πn}{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{arccos ( cos ( \frac{1}{2} ) )}{2} + \frac{2 πn}{2} : π - \frac{1}{4} + πn

\frac{2 π}{2} - \frac{arccos ( cos ( \frac{1}{2} ) )}{2} + \frac{2 πn}{2}

\frac{2 π}{2} = π

\frac{2 π}{2}

数字相除:

\frac{2}{2} = 1

= π

\frac{arccos ( cos ( \frac{1}{2} ) )}{2} = \frac{1}{4}

\frac{arccos ( cos ( \frac{1}{2} ) )}{2}

arccos (cos (\frac{1}{2})) = \frac{1}{2}

arccos (cos (\frac{1}{2}))

对于

0 \leq x \leq π, a rccos (cos (x)) = x

0 \leq \frac{1}{2} \leq π

= \frac{1}{2}

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

使用分式法则:

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

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

数字相乘:

2 \cdot 2 = 4

= \frac{1}{4}

= π - \frac{1}{4} + \frac{2 πn}{2}

\frac{2 πn}{2} = πn

\frac{2 πn}{2}

数字相除:

\frac{2}{2} = 1

= πn

= π - \frac{1}{4} + πn

x = π - \frac{1}{4} + πn

x = π - \frac{1}{4} + πn

x = π - \frac{1}{4} + πn

x = \frac{1}{4} + πn, x = π - \frac{1}{4} + πn

作图

流行的例子

cos (x) = \frac{3}{10}

5 cos (3 x + 60) = 4

3 sin^{2} (x) = 0

sin (x) n = 3

3cos(2x)=4-11cos(x)

3 cos (2 x) = 4 - 11 cos (x)