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人気のある三角関数 >

3cos^2(x)+4cos(x)-4=0

解

3 cos^{2} (x) + 4 cos (x) - 4 = 0

解

x = 0.84106 \dots + 2 πn, x = 2 π - 0.84106 \dots + 2 πn

+1

度

x = 48.18968 \dots^{\circ} + 36 0^{\circ} n, x = 311.81031 \dots^{\circ} + 36 0^{\circ} n

解答ステップ

3 cos^{2} (x) + 4 cos (x) - 4 = 0

置換で解く

3 cos^{2} (x) + 4 cos (x) - 4 = 0

仮定:

cos (x) = u

3 u^{2} + 4 u - 4 = 0

3 u^{2} + 4 u - 4 = 0 : u = \frac{2}{3}, u = - 2

3 u^{2} + 4 u - 4 = 0

解くとthe二次式

3 u^{2} + 4 u - 4 = 0

二次Equationの公式:

次の場合:

a = 3, b = 4, c = - 4

u_{1, 2} = \frac{- 4 \pm 4 ^{2} - 4 \cdot 3 ( - 4 )}{2 \cdot 3}

u_{1, 2} = \frac{- 4 \pm 4 ^{2} - 4 \cdot 3 ( - 4 )}{2 \cdot 3}

4^{2} - 4 \cdot 3 (- 4) = 8

4^{2} - 4 \cdot 3 (- 4)

規則を適用

- (- a) = a

= 4^{2} + 4 \cdot 3 \cdot 4

数を乗じる:

4 \cdot 3 \cdot 4 = 48

= 4^{2} + 48

4^{2} = 16

= 16 + 48

数を足す:

16 + 48 = 64

= 64

数を因数に分解する:

64 = 8^{2}

= 8^{2}

累乗根の規則を適用する:

n a^{n} = a

8^{2} = 8

= 8

u_{1, 2} = \frac{- 4 \pm 8}{2 \cdot 3}

解を分離する

u_{1} = \frac{- 4 + 8}{2 \cdot 3}, u_{2} = \frac{- 4 - 8}{2 \cdot 3}

u = \frac{- 4 + 8}{2 \cdot 3} : \frac{2}{3}

\frac{- 4 + 8}{2 \cdot 3}

数を足す/引く:

- 4 + 8 = 4

= \frac{4}{2 \cdot 3}

数を乗じる:

2 \cdot 3 = 6

= \frac{4}{6}

共通因数を約分する:

2

= \frac{2}{3}

u = \frac{- 4 - 8}{2 \cdot 3} : - 2

\frac{- 4 - 8}{2 \cdot 3}

数を引く:

- 4 - 8 = - 12

= \frac{- 12}{2 \cdot 3}

数を乗じる:

2 \cdot 3 = 6

= \frac{- 12}{6}

分数の規則を適用する:

\frac{- a}{b} = - \frac{a}{b}

= - \frac{12}{6}

数を割る:

\frac{12}{6} = 2

= - 2

二次equationの解:

u = \frac{2}{3}, u = - 2

代用を戻す

u = cos (x)

cos (x) = \frac{2}{3}, cos (x) = - 2

cos (x) = \frac{2}{3}, cos (x) = - 2

cos (x) = \frac{2}{3} : x = arccos (\frac{2}{3}) + 2 πn, x = 2 π - arccos (\frac{2}{3}) + 2 πn

cos (x) = \frac{2}{3}

三角関数の逆数プロパティを適用する

cos (x) = \frac{2}{3}

以下の一般解

cos (x) = \frac{2}{3}

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

x = arccos (\frac{2}{3}) + 2 πn, x = 2 π - arccos (\frac{2}{3}) + 2 πn

x = arccos (\frac{2}{3}) + 2 πn, x = 2 π - arccos (\frac{2}{3}) + 2 πn

cos (x) = - 2 :

解なし

cos (x) = - 2

- 1 \leq cos (x) \leq 1

解なし

すべての解を組み合わせる

x = arccos (\frac{2}{3}) + 2 πn, x = 2 π - arccos (\frac{2}{3}) + 2 πn

10進法形式で解を証明する

x = 0.84106 \dots + 2 πn, x = 2 π - 0.84106 \dots + 2 πn

グラフ

人気の例

sin(θ)=-27/190

sin (θ) = - \frac{27}{190}

4sin(θ)=1+sin(θ)

4 sin (θ) = 1 + sin (θ)

tan(θ)-sqrt(3)=0,0<= θ<= 2pi

tan (θ) - 3 = 0, 0 \leq θ \leq 2 π

1/32*1200^2*sin(2θ)=3000

\frac{1}{32} \cdot 120 0^{2} \cdot sin (2 θ) = 3000

1-cos^2(a)=sin^2(2a)

1 - cos^{2} (a) = sin^{2} (2 a)