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人気のある三角関数 >

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

解

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

解

x = 0.81462 \dots + 2 πn, x = 2 π - 0.81462 \dots + 2 πn

+1

度

x = 46.67462 \dots^{\circ} + 36 0^{\circ} n, x = 313.32537 \dots^{\circ} + 36 0^{\circ} n

解答ステップ

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

置換で解く

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

仮定:

cos (x) = u

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

2 u^{2} + 3 u - 3 = 0 : u = \frac{- 3 + 33}{4}, u = \frac{- 3 - 33}{4}

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

解くとthe二次式

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

二次Equationの公式:

次の場合:

a = 2, b = 3, c = - 3

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

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

3^{2} - 4 \cdot 2 (- 3) = 33

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

規則を適用

- (- a) = a

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

数を乗じる:

4 \cdot 2 \cdot 3 = 24

= 3^{2} + 24

3^{2} = 9

= 9 + 24

数を足す:

9 + 24 = 33

= 33

u_{1, 2} = \frac{- 3 \pm 33}{2 \cdot 2}

解を分離する

u_{1} = \frac{- 3 + 33}{2 \cdot 2}, u_{2} = \frac{- 3 - 33}{2 \cdot 2}

u = \frac{- 3 + 33}{2 \cdot 2} : \frac{- 3 + 33}{4}

\frac{- 3 + 33}{2 \cdot 2}

数を乗じる:

2 \cdot 2 = 4

= \frac{- 3 + 33}{4}

u = \frac{- 3 - 33}{2 \cdot 2} : \frac{- 3 - 33}{4}

\frac{- 3 - 33}{2 \cdot 2}

数を乗じる:

2 \cdot 2 = 4

= \frac{- 3 - 33}{4}

二次equationの解:

u = \frac{- 3 + 33}{4}, u = \frac{- 3 - 33}{4}

代用を戻す

u = cos (x)

cos (x) = \frac{- 3 + 33}{4}, cos (x) = \frac{- 3 - 33}{4}

cos (x) = \frac{- 3 + 33}{4}, cos (x) = \frac{- 3 - 33}{4}

cos (x) = \frac{- 3 + 33}{4} : x = arccos (\frac{- 3 + 33}{4}) + 2 πn, x = 2 π - arccos (\frac{- 3 + 33}{4}) + 2 πn

cos (x) = \frac{- 3 + 33}{4}

三角関数の逆数プロパティを適用する

cos (x) = \frac{- 3 + 33}{4}

以下の一般解

cos (x) = \frac{- 3 + 33}{4}

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

x = arccos (\frac{- 3 + 33}{4}) + 2 πn, x = 2 π - arccos (\frac{- 3 + 33}{4}) + 2 πn

x = arccos (\frac{- 3 + 33}{4}) + 2 πn, x = 2 π - arccos (\frac{- 3 + 33}{4}) + 2 πn

cos (x) = \frac{- 3 - 33}{4} :

解なし

cos (x) = \frac{- 3 - 33}{4}

- 1 \leq cos (x) \leq 1

解なし

すべての解を組み合わせる

x = arccos (\frac{- 3 + 33}{4}) + 2 πn, x = 2 π - arccos (\frac{- 3 + 33}{4}) + 2 πn

10進法形式で解を証明する

x = 0.81462 \dots + 2 πn, x = 2 π - 0.81462 \dots + 2 πn

グラフ

人気の例

3sin(x)-5cos(x)=0

3 sin (x) - 5 cos (x) = 0

sin^{2} (x) = 0.85

cos(x-60)=(sqrt(3))/2

cos (x - 6 0^{\circ}) = \frac{3}{2}

(0.5*9.8*l(1-cos(θ)))=0.018

(0.5 \cdot 9.8 \cdot l (1 - cos (θ))) = 0.018

solvefor x,0=-sin(2x)-2cos(x)

so l v e f or x, 0 = - sin (2 x) - 2 cos (x)