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受欢迎的三角函数 >

0.6=cos^2(x)

解答

0.6 = cos^{2} (x)

解答

x = 0.68471 \dots + 2 πn, x = 2 π - 0.68471 \dots + 2 πn, x = 2.45687 \dots + 2 πn, x = - 2.45687 \dots + 2 πn

+1

度数

x = 39.23152 \dots^{\circ} + 36 0^{\circ} n, x = 320.76847 \dots^{\circ} + 36 0^{\circ} n, x = 140.76847 \dots^{\circ} + 36 0^{\circ} n, x = - 140.76847 \dots^{\circ} + 36 0^{\circ} n

求解步骤

0.6 = cos^{2} (x)

交换两边

cos^{2} (x) = 0.6

用替代法求解

cos^{2} (x) = 0.6

令

: cos (x) = u

u^{2} = 0.6

u^{2} = 0.6 : u = 0.6, u = - 0.6

u^{2} = 0.6

对于

x^{2} = f (a)

解为

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

u = 0.6, u = - 0.6

u = cos (x)

代回

cos (x) = 0.6, cos (x) = - 0.6

cos (x) = 0.6, cos (x) = - 0.6

cos (x) = 0.6 : x = arccos (0.6) + 2 πn, x = 2 π - arccos (0.6) + 2 πn

cos (x) = 0.6

使用反三角函数性质

cos (x) = 0.6

cos (x) = 0.6

的通解

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

x = arccos (0.6) + 2 πn, x = 2 π - arccos (0.6) + 2 πn

x = arccos (0.6) + 2 πn, x = 2 π - arccos (0.6) + 2 πn

cos (x) = - 0.6 : x = arccos (- 0.6) + 2 πn, x = - arccos (- 0.6) + 2 πn

cos (x) = - 0.6

使用反三角函数性质

cos (x) = - 0.6

cos (x) = - 0.6

的通解

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

x = arccos (- 0.6) + 2 πn, x = - arccos (- 0.6) + 2 πn

x = arccos (- 0.6) + 2 πn, x = - arccos (- 0.6) + 2 πn

合并所有解

x = arccos (0.6) + 2 πn, x = 2 π - arccos (0.6) + 2 πn, x = arccos (- 0.6) + 2 πn, x = - arccos (- 0.6) + 2 πn

以小数形式表示解

x = 0.68471 \dots + 2 πn, x = 2 π - 0.68471 \dots + 2 πn, x = 2.45687 \dots + 2 πn, x = - 2.45687 \dots + 2 πn

作图

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