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受欢迎的三角函数 >

cos^2(x)=0.75

解答

cos^{2} (x) = 0.75

解答

x = 0.52359 \dots + 2 πn, x = 2 π - 0.52359 \dots + 2 πn, x = 2.61799 \dots + 2 πn, x = - 2.61799 \dots + 2 πn

+1

度数

x = 3 0^{\circ} + 36 0^{\circ} n, x = 329.99999 \dots^{\circ} + 36 0^{\circ} n, x = 15 0^{\circ} + 36 0^{\circ} n, x = - 15 0^{\circ} + 36 0^{\circ} n

求解步骤

cos^{2} (x) = 0.75

用替代法求解

cos^{2} (x) = 0.75

令

: cos (x) = u

u^{2} = 0.75

u^{2} = 0.75 : u = 0.75, u = - 0.75

u^{2} = 0.75

对于

x^{2} = f (a)

解为

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

u = 0.75, u = - 0.75

u = cos (x)

代回

cos (x) = 0.75, cos (x) = - 0.75

cos (x) = 0.75, cos (x) = - 0.75

cos (x) = 0.75 : x = arccos (0.75) + 2 πn, x = 2 π - arccos (0.75) + 2 πn

cos (x) = 0.75

使用反三角函数性质

cos (x) = 0.75

cos (x) = 0.75

的通解

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

x = arccos (0.75) + 2 πn, x = 2 π - arccos (0.75) + 2 πn

x = arccos (0.75) + 2 πn, x = 2 π - arccos (0.75) + 2 πn

cos (x) = - 0.75 : x = arccos (- 0.75) + 2 πn, x = - arccos (- 0.75) + 2 πn

cos (x) = - 0.75

使用反三角函数性质

cos (x) = - 0.75

cos (x) = - 0.75

的通解

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

x = arccos (- 0.75) + 2 πn, x = - arccos (- 0.75) + 2 πn

x = arccos (- 0.75) + 2 πn, x = - arccos (- 0.75) + 2 πn

合并所有解

x = arccos (0.75) + 2 πn, x = 2 π - arccos (0.75) + 2 πn, x = arccos (- 0.75) + 2 πn, x = - arccos (- 0.75) + 2 πn

以小数形式表示解

x = 0.52359 \dots + 2 πn, x = 2 π - 0.52359 \dots + 2 πn, x = 2.61799 \dots + 2 πn, x = - 2.61799 \dots + 2 πn

作图

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