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受欢迎的三角函数 >

cos^2(x)= 1/3

解答

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

解答

x = 0.95531 \dots + 2 πn, x = 2 π - 0.95531 \dots + 2 πn, x = 2.18627 \dots + 2 πn, x = - 2.18627 \dots + 2 πn

+1

度数

x = 54.73561 \dots^{\circ} + 36 0^{\circ} n, x = 305.26438 \dots^{\circ} + 36 0^{\circ} n, x = 125.26438 \dots^{\circ} + 36 0^{\circ} n, x = - 125.26438 \dots^{\circ} + 36 0^{\circ} n

求解步骤

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

用替代法求解

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

令

: cos (x) = u

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

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

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

对于

x^{2} = f (a)

解为

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

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

u = cos (x)

代回

cos (x) = \frac{1}{3}, cos (x) = - \frac{1}{3}

cos (x) = \frac{1}{3}, cos (x) = - \frac{1}{3}

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

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

使用反三角函数性质

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

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

的通解

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

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

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

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

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

使用反三角函数性质

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

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

的通解

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

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

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

合并所有解

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

以小数形式表示解

x = 0.95531 \dots + 2 πn, x = 2 π - 0.95531 \dots + 2 πn, x = 2.18627 \dots + 2 πn, x = - 2.18627 \dots + 2 πn

作图

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