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受欢迎的三角函数 >

2cos^2(x)-1.28=0

解答

2 cos^{2} (x) - 1.28 = 0

解答

x = 0.64350 \dots + 2 πn, x = 2 π - 0.64350 \dots + 2 πn, x = 2.49809 \dots + 2 πn, x = - 2.49809 \dots + 2 πn

+1

度数

x = 36.86989 \dots^{\circ} + 36 0^{\circ} n, x = 323.13010 \dots^{\circ} + 36 0^{\circ} n, x = 143.13010 \dots^{\circ} + 36 0^{\circ} n, x = - 143.13010 \dots^{\circ} + 36 0^{\circ} n

求解步骤

2 cos^{2} (x) - 1.28 = 0

用替代法求解

2 cos^{2} (x) - 1.28 = 0

令

: cos (x) = u

2 u^{2} - 1.28 = 0

2 u^{2} - 1.28 = 0 : u = 0.64, u = - 0.64

2 u^{2} - 1.28 = 0

将

1.28

到右边

2 u^{2} - 1.28 = 0

两边加上

1.28

2 u^{2} - 1.28 + 1.28 = 0 + 1.28

化简

2 u^{2} = 1.28

2 u^{2} = 1.28

两边除以

2

2 u^{2} = 1.28

两边除以

2

\frac{2 u ^{2}}{2} = \frac{1.28}{2}

化简

u^{2} = 0.64

u^{2} = 0.64

对于

x^{2} = f (a)

解为

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

u = 0.64, u = - 0.64

u = cos (x)

代回

cos (x) = 0.64, cos (x) = - 0.64

cos (x) = 0.64, cos (x) = - 0.64

cos (x) = 0.64 : x = arccos (0.64) + 2 πn, x = 2 π - arccos (0.64) + 2 πn

cos (x) = 0.64

使用反三角函数性质

cos (x) = 0.64

cos (x) = 0.64

的通解

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

x = arccos (0.64) + 2 πn, x = 2 π - arccos (0.64) + 2 πn

x = arccos (0.64) + 2 πn, x = 2 π - arccos (0.64) + 2 πn

cos (x) = - 0.64 : x = arccos (- 0.64) + 2 πn, x = - arccos (- 0.64) + 2 πn

cos (x) = - 0.64

使用反三角函数性质

cos (x) = - 0.64

cos (x) = - 0.64

的通解

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

x = arccos (- 0.64) + 2 πn, x = - arccos (- 0.64) + 2 πn

x = arccos (- 0.64) + 2 πn, x = - arccos (- 0.64) + 2 πn

合并所有解

x = arccos (0.64) + 2 πn, x = 2 π - arccos (0.64) + 2 πn, x = arccos (- 0.64) + 2 πn, x = - arccos (- 0.64) + 2 πn

以小数形式表示解

x = 0.64350 \dots + 2 πn, x = 2 π - 0.64350 \dots + 2 πn, x = 2.49809 \dots + 2 πn, x = - 2.49809 \dots + 2 πn

作图

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