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受欢迎的三角函数 >

cos(x)= 2/(sqrt(6))

解答

cos (x) = \frac{2}{6}

解答

x = 0.61547 \dots + 2 πn, x = 2 π - 0.61547 \dots + 2 πn

+1

弧度

x = 0.61547 \dots + 6.28318 \dots n, x = 5.66770 \dots + 6.28318 \dots n

求解步骤

cos (x) = \frac{2}{6}

化简

\frac{2}{6} : \frac{2}{3}

\frac{2}{6}

分解

6 : 23

因式分解

6 = 2 \cdot 3

= 2 \cdot 3

使用根式运算法则:

n ab = n a n b

= 23

= \frac{2}{2 3}

消掉

\frac{2}{2 3} : \frac{2}{3}

\frac{2}{2 3}

使用根式运算法则:

n a = a^{\frac{1}{n}}

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

= \frac{2}{2 ^{\frac{1}{2}} 3}

使用指数法则:

\frac{x ^{a}}{x ^{b}} = x^{a - b}

\frac{2 ^{1}}{2 ^{\frac{1}{2}}} = 2^{1 - \frac{1}{2}}

= \frac{2 ^{1 - \frac{1}{2}}}{3}

数字相减:

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

= \frac{2 ^{\frac{1}{2}}}{3}

使用根式运算法则:

a^{\frac{1}{n}} = n a

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

= \frac{2}{3}

= \frac{2}{3}

合并相同指数项 :

\frac{x}{y} = \frac{x}{y}

= \frac{2}{3}

使用反三角函数性质

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

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

的通解

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

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

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

以小数形式表示解

x = 0.61547 \dots + 2 πn, x = 2 π - 0.61547 \dots + 2 πn

作图

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