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受欢迎的三角函数 >

cos(2x)=1-2(3/5)^2

解答

cos (2 x) = 1 - 2 (\frac{3}{5})^{2}

解答

x = \frac{1.28700 \dots}{2} + πn, x = π - \frac{1.28700 \dots}{2} + πn

+1

弧度

x = 0.64350 \dots + πn, x = π - 0.64350 \dots + πn

求解步骤

cos (2 x) = 1 - 2 (\frac{3}{5})^{2}

化简

1 - 2 (\frac{3}{5})^{2} : \frac{7}{25}

1 - 2 (\frac{3}{5})^{2}

2 (\frac{3}{5})^{2} = \frac{18}{25}

2 (\frac{3}{5})^{2}

(\frac{3}{5})^{2} = \frac{3 ^{2}}{5 ^{2}}

(\frac{3}{5})^{2}

使用指数法则:

(\frac{a}{b})^{c} = \frac{a ^{c}}{b ^{c}}

= \frac{3 ^{2}}{5 ^{2}}

= 2 \cdot \frac{3 ^{2}}{5 ^{2}}

分式相乘:

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

= \frac{3 ^{2} \cdot 2}{5 ^{2}}

3^{2} \cdot 2 = 18

3^{2} \cdot 2

3^{2} = 9

= 9 \cdot 2

数字相乘:

9 \cdot 2 = 18

= 18

= \frac{18}{5 ^{2}}

5^{2} = 25

= \frac{18}{25}

= 1 - \frac{18}{25}

将项转换为分式:

1 = \frac{1 \cdot 25}{25}

= \frac{1 \cdot 25}{25} - \frac{18}{25}

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{1 \cdot 25 - 18}{25}

1 \cdot 25 - 18 = 7

1 \cdot 25 - 18

数字相乘:

1 \cdot 25 = 25

= 25 - 18

数字相减:

25 - 18 = 7

= 7

= \frac{7}{25}

使用反三角函数性质

cos (2 x) = \frac{7}{25}

cos (2 x) = \frac{7}{25}

的通解

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

2 x = arccos (\frac{7}{25}) + 2 πn, 2 x = 2 π - arccos (\frac{7}{25}) + 2 πn

2 x = arccos (\frac{7}{25}) + 2 πn, 2 x = 2 π - arccos (\frac{7}{25}) + 2 πn

解

2 x = arccos (\frac{7}{25}) + 2 πn : x = \frac{arccos ( \frac{7}{25} )}{2} + πn

2 x = arccos (\frac{7}{25}) + 2 πn

两边除以

2

2 x = arccos (\frac{7}{25}) + 2 πn

两边除以

2

\frac{2 x}{2} = \frac{arccos ( \frac{7}{25} )}{2} + \frac{2 πn}{2}

化简

x = \frac{arccos ( \frac{7}{25} )}{2} + πn

x = \frac{arccos ( \frac{7}{25} )}{2} + πn

解

2 x = 2 π - arccos (\frac{7}{25}) + 2 πn : x = π - \frac{arccos ( \frac{7}{25} )}{2} + πn

2 x = 2 π - arccos (\frac{7}{25}) + 2 πn

两边除以

2

2 x = 2 π - arccos (\frac{7}{25}) + 2 πn

两边除以

2

\frac{2 x}{2} = \frac{2 π}{2} - \frac{arccos ( \frac{7}{25} )}{2} + \frac{2 πn}{2}

化简

x = π - \frac{arccos ( \frac{7}{25} )}{2} + πn

x = π - \frac{arccos ( \frac{7}{25} )}{2} + πn

x = \frac{arccos ( \frac{7}{25} )}{2} + πn, x = π - \frac{arccos ( \frac{7}{25} )}{2} + πn

以小数形式表示解

x = \frac{1.28700 \dots}{2} + πn, x = π - \frac{1.28700 \dots}{2} + πn

作图

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