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受欢迎的三角函数 >

cos^2(x)=((8k-9))/2

解答

cos^{2} (x) = \frac{( 8 k - 9 )}{2}

解答

x = arccos (\frac{8 k - 9}{2}) + 2 πn, x = - arccos (\frac{8 k - 9}{2}) + 2 πn, x = arccos (- \frac{8 k - 9}{2}) + 2 πn, x = - arccos (- \frac{8 k - 9}{2}) + 2 πn

求解步骤

cos^{2} (x) = \frac{( 8 k - 9 )}{2}

用替代法求解

cos^{2} (x) = \frac{8 k - 9}{2}

令

: cos (x) = u

u^{2} = \frac{8 k - 9}{2}

u^{2} = \frac{8 k - 9}{2} : u = \frac{8 k - 9}{2}, u = - \frac{8 k - 9}{2}

u^{2} = \frac{8 k - 9}{2}

对于

x^{2} = f (a)

解为

x = f (a), - f (a)

u = \frac{8 k - 9}{2}, u = - \frac{8 k - 9}{2}

u = cos (x)

代回

cos (x) = \frac{8 k - 9}{2}, cos (x) = - \frac{8 k - 9}{2}

cos (x) = \frac{8 k - 9}{2}, cos (x) = - \frac{8 k - 9}{2}

cos (x) = \frac{8 k - 9}{2} : x = arccos (\frac{8 k - 9}{2}) + 2 πn, x = - arccos (\frac{8 k - 9}{2}) + 2 πn

cos (x) = \frac{8 k - 9}{2}

使用反三角函数性质

cos (x) = \frac{8 k - 9}{2}

cos (x) = \frac{8 k - 9}{2}

的通解

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

x = arccos (\frac{8 k - 9}{2}) + 2 πn, x = - arccos (\frac{8 k - 9}{2}) + 2 πn

x = arccos (\frac{8 k - 9}{2}) + 2 πn, x = - arccos (\frac{8 k - 9}{2}) + 2 πn

cos (x) = - \frac{8 k - 9}{2} : x = arccos (- \frac{8 k - 9}{2}) + 2 πn, x = - arccos (- \frac{8 k - 9}{2}) + 2 πn

cos (x) = - \frac{8 k - 9}{2}

使用反三角函数性质

cos (x) = - \frac{8 k - 9}{2}

cos (x) = - \frac{8 k - 9}{2}

的通解

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

x = arccos (- \frac{8 k - 9}{2}) + 2 πn, x = - arccos (- \frac{8 k - 9}{2}) + 2 πn

x = arccos (- \frac{8 k - 9}{2}) + 2 πn, x = - arccos (- \frac{8 k - 9}{2}) + 2 πn

合并所有解

x = arccos (\frac{8 k - 9}{2}) + 2 πn, x = - arccos (\frac{8 k - 9}{2}) + 2 πn, x = arccos (- \frac{8 k - 9}{2}) + 2 πn, x = - arccos (- \frac{8 k - 9}{2}) + 2 πn

作图

流行的例子

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