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受欢迎的三角函数 >

cos^2(θ)+(5^2cos(θ))/(9.81(8))-1=0

解答

cos^{2} (θ) + \frac{5 ^{2} cos ( θ )}{9.81 ( 8 )} - 1 = 0

解答

θ = 0.54845 \dots + 2 πn, θ = 2 π - 0.54845 \dots + 2 πn

+1

度数

θ = 31.42440 \dots^{\circ} + 36 0^{\circ} n, θ = 328.57559 \dots^{\circ} + 36 0^{\circ} n

求解步骤

cos^{2} (θ) + \frac{5 ^{2} cos ( θ )}{9.81 ( 8 )} - 1 = 0

用替代法求解

cos^{2} (θ) + \frac{5 ^{2} cos ( θ )}{9.81 \cdot 8} - 1 = 0

令

: cos (θ) = u

u^{2} + \frac{5 ^{2} u}{9.81 \cdot 8} - 1 = 0

u^{2} + \frac{5 ^{2} u}{9.81 \cdot 8} - 1 = 0 : u = \frac{- 25 + 25261.4416}{156.96}, u = \frac{- 25 - 25261.4416}{156.96}

u^{2} + \frac{5 ^{2} u}{9.81 \cdot 8} - 1 = 0

化简

9.81 \cdot 8 : 78.48

9.81 \cdot 8

数字相乘:

9.81 \cdot 8 = 78.48

= 78.48

u^{2} + \frac{5 ^{2} u}{78.48} - 1 = 0

在两边乘以

78.48

u^{2} + \frac{5 ^{2} u}{78.48} - 1 = 0

在两边乘以

78.48

u^{2} \cdot 78.48 + \frac{5 ^{2} u}{78.48} \cdot 78.48 - 1 \cdot 78.48 = 0 \cdot 78.48

化简

78.48 u^{2} + 25 u - 78.48 = 0

78.48 u^{2} + 25 u - 78.48 = 0

使用求根公式求解

78.48 u^{2} + 25 u - 78.48 = 0

二次方程求根公式:

若

a = 78.48, b = 25, c = - 78.48

u_{1, 2} = \frac{- 25 \pm 2 5 ^{2} - 4 \cdot 78.48 ( - 78.48 )}{2 \cdot 78.48}

u_{1, 2} = \frac{- 25 \pm 2 5 ^{2} - 4 \cdot 78.48 ( - 78.48 )}{2 \cdot 78.48}

2 5^{2} - 4 \cdot 78.48 (- 78.48) = 25261.4416

2 5^{2} - 4 \cdot 78.48 (- 78.48)

使用法则

- (- a) = a

= 2 5^{2} + 4 \cdot 78.48 \cdot 78.48

数字相乘:

4 \cdot 78.48 \cdot 78.48 = 24636.4416

= 2 5^{2} + 24636.4416

2 5^{2} = 625

= 625 + 24636.4416

数字相加:

625 + 24636.4416 = 25261.4416

= 25261.4416

u_{1, 2} = \frac{- 25 \pm 25261.4416}{2 \cdot 78.48}

将解分隔开

u_{1} = \frac{- 25 + 25261.4416}{2 \cdot 78.48}, u_{2} = \frac{- 25 - 25261.4416}{2 \cdot 78.48}

u = \frac{- 25 + 25261.4416}{2 \cdot 78.48} : \frac{- 25 + 25261.4416}{156.96}

\frac{- 25 + 25261.4416}{2 \cdot 78.48}

数字相乘:

2 \cdot 78.48 = 156.96

= \frac{- 25 + 25261.4416}{156.96}

u = \frac{- 25 - 25261.4416}{2 \cdot 78.48} : \frac{- 25 - 25261.4416}{156.96}

\frac{- 25 - 25261.4416}{2 \cdot 78.48}

数字相乘:

2 \cdot 78.48 = 156.96

= \frac{- 25 - 25261.4416}{156.96}

二次方程组的解是:

u = \frac{- 25 + 25261.4416}{156.96}, u = \frac{- 25 - 25261.4416}{156.96}

u = cos (θ)

代回

cos (θ) = \frac{- 25 + 25261.4416}{156.96}, cos (θ) = \frac{- 25 - 25261.4416}{156.96}

cos (θ) = \frac{- 25 + 25261.4416}{156.96}, cos (θ) = \frac{- 25 - 25261.4416}{156.96}

cos (θ) = \frac{- 25 + 25261.4416}{156.96} : θ = arccos (\frac{- 25 + 25261.4416}{156.96}) + 2 πn, θ = 2 π - arccos (\frac{- 25 + 25261.4416}{156.96}) + 2 πn

cos (θ) = \frac{- 25 + 25261.4416}{156.96}

使用反三角函数性质

cos (θ) = \frac{- 25 + 25261.4416}{156.96}

cos (θ) = \frac{- 25 + 25261.4416}{156.96}

的通解

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

θ = arccos (\frac{- 25 + 25261.4416}{156.96}) + 2 πn, θ = 2 π - arccos (\frac{- 25 + 25261.4416}{156.96}) + 2 πn

θ = arccos (\frac{- 25 + 25261.4416}{156.96}) + 2 πn, θ = 2 π - arccos (\frac{- 25 + 25261.4416}{156.96}) + 2 πn

cos (θ) = \frac{- 25 - 25261.4416}{156.96} :

无解

cos (θ) = \frac{- 25 - 25261.4416}{156.96}

- 1 \leq cos (x) \leq 1

无解

合并所有解

θ = arccos (\frac{- 25 + 25261.4416}{156.96}) + 2 πn, θ = 2 π - arccos (\frac{- 25 + 25261.4416}{156.96}) + 2 πn

以小数形式表示解

θ = 0.54845 \dots + 2 πn, θ = 2 π - 0.54845 \dots + 2 πn

作图

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