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受欢迎的三角函数 >

-cos(2x)=2cos(2x)-1

解答

- cos (2 x) = 2 cos (2 x) - 1

解答

x = \frac{1.23095 \dots}{2} + πn, x = π - \frac{1.23095 \dots}{2} + πn

+1

度数

x = 35.26438 \dots^{\circ} + 18 0^{\circ} n, x = 144.73561 \dots^{\circ} + 18 0^{\circ} n

求解步骤

- cos (2 x) = 2 cos (2 x) - 1

用替代法求解

- cos (2 x) = 2 cos (2 x) - 1

令

: cos (2 x) = u

- u = 2 u - 1

- u = 2 u - 1 : u = \frac{1}{3}

- u = 2 u - 1

将

2 u

para o lado esquerdo

- u = 2 u - 1

两边减去

2 u

- u - 2 u = 2 u - 1 - 2 u

化简

- 3 u = - 1

- 3 u = - 1

两边除以

- 3

- 3 u = - 1

两边除以

- 3

\frac{- 3 u}{- 3} = \frac{- 1}{- 3}

化简

u = \frac{1}{3}

u = \frac{1}{3}

u = cos (2 x)

代回

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

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

cos (2 x) = \frac{1}{3} : x = \frac{arccos ( \frac{1}{3} )}{2} + πn, x = π - \frac{arccos ( \frac{1}{3} )}{2} + πn

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

使用反三角函数性质

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

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

的通解

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

2 x = arccos (\frac{1}{3}) + 2 πn, 2 x = 2 π - arccos (\frac{1}{3}) + 2 πn

2 x = arccos (\frac{1}{3}) + 2 πn, 2 x = 2 π - arccos (\frac{1}{3}) + 2 πn

解

2 x = arccos (\frac{1}{3}) + 2 πn : x = \frac{arccos ( \frac{1}{3} )}{2} + πn

2 x = arccos (\frac{1}{3}) + 2 πn

两边除以

2

2 x = arccos (\frac{1}{3}) + 2 πn

两边除以

2

\frac{2 x}{2} = \frac{arccos ( \frac{1}{3} )}{2} + \frac{2 πn}{2}

化简

x = \frac{arccos ( \frac{1}{3} )}{2} + πn

x = \frac{arccos ( \frac{1}{3} )}{2} + πn

解

2 x = 2 π - arccos (\frac{1}{3}) + 2 πn : x = π - \frac{arccos ( \frac{1}{3} )}{2} + πn

2 x = 2 π - arccos (\frac{1}{3}) + 2 πn

两边除以

2

2 x = 2 π - arccos (\frac{1}{3}) + 2 πn

两边除以

2

\frac{2 x}{2} = \frac{2 π}{2} - \frac{arccos ( \frac{1}{3} )}{2} + \frac{2 πn}{2}

化简

x = π - \frac{arccos ( \frac{1}{3} )}{2} + πn

x = π - \frac{arccos ( \frac{1}{3} )}{2} + πn

x = \frac{arccos ( \frac{1}{3} )}{2} + πn, x = π - \frac{arccos ( \frac{1}{3} )}{2} + πn

合并所有解

x = \frac{arccos ( \frac{1}{3} )}{2} + πn, x = π - \frac{arccos ( \frac{1}{3} )}{2} + πn

以小数形式表示解

x = \frac{1.23095 \dots}{2} + πn, x = π - \frac{1.23095 \dots}{2} + πn

作图

流行的例子

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sin(A)=(sqrt(3))/2

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