ja

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

人気のある三角関数 >

cos^2(θ)+(5^2cos(θ))/(9.81(8))-1=0

解

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

解

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

+1

度

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

解答ステップ

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

置換で解く

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

仮定:

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

簡素化

9.81 \cdot 8 : 78.48

9.81 \cdot 8

数を乗じる:

9.81 \cdot 8 = 78.48

= 78.48

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

以下で両辺を乗じる:

78.48

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

以下で両辺を乗じる:

78.48

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

簡素化

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

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

解くとthe二次式

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

二次Equationの公式:

次の場合:

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)

規則を適用

- (- a) = a

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

数を乗じる:

4 \cdot 78.48 \cdot 78.48 = 24636.4416

= 2 5^{2} + 24636.4416

2 5^{2} = 625

= 625 + 24636.4416

数を足す:

625 + 24636.4416 = 25261.4416

= 25261.4416

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

解を分離する

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}

数を乗じる:

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}

数を乗じる:

2 \cdot 78.48 = 156.96

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

二次equationの解:

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

代用を戻す

u = cos (θ)

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}

三角関数の逆数プロパティを適用する

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

以下の一般解

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

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} :

解なし

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

- 1 \leq cos (x) \leq 1

解なし

すべての解を組み合わせる

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

10進法形式で解を証明する

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

グラフ

人気の例

105=100+30sin((12pi)/5 t)

105 = 100 + 30 sin (\frac{12 π}{5} t)

3/(sin(x))= 1/(cos(x))

\frac{3}{sin ( x )} = \frac{1}{cos ( x )}

2cos(t)-2sin(2t)=0

2 cos (t) - 2 sin (2 t) = 0

4sin(x)=-2cos(x)

4 sin (x) = - 2 cos (x)

3 sin (2 x) = 1.5