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受欢迎的三角函数 >

solvefor k,6(-cos(k/2)+1)=1.5

解答

求解

k, 6 (- cos (\frac{k}{2}) + 1) = 1.5

解答

k = 2 \cdot 0.72273 \dots + 4 πn, k = 4 π - 2 \cdot 0.72273 \dots + 4 πn

+1

度数

k = 82.81924 \dots^{\circ} + 72 0^{\circ} n, k = 637.18075 \dots^{\circ} + 72 0^{\circ} n

求解步骤

6 (- cos (\frac{k}{2}) + 1) = 1.5

两边除以

6

6 (- cos (\frac{k}{2}) + 1) = 1.5

两边除以

6

\frac{6 ( - cos ( \frac{k}{2} ) + 1 )}{6} = \frac{1.5}{6}

化简

- cos (\frac{k}{2}) + 1 = 0.25

- cos (\frac{k}{2}) + 1 = 0.25

将

1

到右边

- cos (\frac{k}{2}) + 1 = 0.25

两边减去

1

- cos (\frac{k}{2}) + 1 - 1 = 0.25 - 1

化简

- cos (\frac{k}{2}) = - 0.75

- cos (\frac{k}{2}) = - 0.75

两边除以

- 1

- cos (\frac{k}{2}) = - 0.75

两边除以

- 1

\frac{- cos ( \frac{k}{2} )}{- 1} = \frac{- 0.75}{- 1}

化简

cos (\frac{k}{2}) = 0.75

cos (\frac{k}{2}) = 0.75

使用反三角函数性质

cos (\frac{k}{2}) = 0.75

cos (\frac{k}{2}) = 0.75

的通解

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

\frac{k}{2} = arccos (0.75) + 2 πn, \frac{k}{2} = 2 π - arccos (0.75) + 2 πn

\frac{k}{2} = arccos (0.75) + 2 πn, \frac{k}{2} = 2 π - arccos (0.75) + 2 πn

解

\frac{k}{2} = arccos (0.75) + 2 πn : k = 2 arccos (0.75) + 4 πn

\frac{k}{2} = arccos (0.75) + 2 πn

在两边乘以

2

\frac{k}{2} = arccos (0.75) + 2 πn

在两边乘以

2

\frac{2 k}{2} = 2 arccos (0.75) + 2 \cdot 2 πn

化简

k = 2 arccos (0.75) + 4 πn

k = 2 arccos (0.75) + 4 πn

解

\frac{k}{2} = 2 π - arccos (0.75) + 2 πn : k = 4 π - 2 arccos (0.75) + 4 πn

\frac{k}{2} = 2 π - arccos (0.75) + 2 πn

在两边乘以

2

\frac{k}{2} = 2 π - arccos (0.75) + 2 πn

在两边乘以

2

\frac{2 k}{2} = 2 \cdot 2 π - 2 arccos (0.75) + 2 \cdot 2 πn

化简

k = 4 π - 2 arccos (0.75) + 4 πn

k = 4 π - 2 arccos (0.75) + 4 πn

k = 2 arccos (0.75) + 4 πn, k = 4 π - 2 arccos (0.75) + 4 πn

以小数形式表示解

k = 2 \cdot 0.72273 \dots + 4 πn, k = 4 π - 2 \cdot 0.72273 \dots + 4 πn

作图

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