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人気のある三角関数 >

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

解

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

解

x = \frac{π}{2} + 2 πn, x = \frac{3 π}{2} + 2 πn

+1

度

x = 9 0^{\circ} + 36 0^{\circ} n, x = 27 0^{\circ} + 36 0^{\circ} n

解答ステップ

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

置換で解く

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

仮定:

cos (x) = u

2 u - u^{2} = 0

2 u - u^{2} = 0 : u = 0, u = 2

2 u - u^{2} = 0

標準的な形式で書く

a x^{2} + b x + c = 0

- u^{2} + 2 u = 0

解くとthe二次式

- u^{2} + 2 u = 0

二次Equationの公式:

次の場合:

a = - 1, b = 2, c = 0

u_{1, 2} = \frac{- 2 \pm 2 ^{2} - 4 ( - 1 ) \cdot 0}{2 ( - 1 )}

u_{1, 2} = \frac{- 2 \pm 2 ^{2} - 4 ( - 1 ) \cdot 0}{2 ( - 1 )}

2^{2} - 4 (- 1) \cdot 0 = 2

2^{2} - 4 (- 1) \cdot 0

規則を適用

- (- a) = a

= 2^{2} + 4 \cdot 1 \cdot 0

規則を適用

0 \cdot a = 0

= 2^{2} + 0

2^{2} + 0 = 2^{2}

= 2^{2}

累乗根の規則を適用する:

n a^{n} = a,

, 以下を想定

a \geq 0

= 2

u_{1, 2} = \frac{- 2 \pm 2}{2 ( - 1 )}

解を分離する

u_{1} = \frac{- 2 + 2}{2 ( - 1 )}, u_{2} = \frac{- 2 - 2}{2 ( - 1 )}

u = \frac{- 2 + 2}{2 ( - 1 )} : 0

\frac{- 2 + 2}{2 ( - 1 )}

括弧を削除する:

(- a) = - a

= \frac{- 2 + 2}{- 2 \cdot 1}

数を足す/引く:

- 2 + 2 = 0

= \frac{0}{- 2 \cdot 1}

数を乗じる:

2 \cdot 1 = 2

= \frac{0}{- 2}

分数の規則を適用する:

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

= - \frac{0}{2}

規則を適用

\frac{0}{a} = 0, a \neq = 0

= - 0

= 0

u = \frac{- 2 - 2}{2 ( - 1 )} : 2

\frac{- 2 - 2}{2 ( - 1 )}

括弧を削除する:

(- a) = - a

= \frac{- 2 - 2}{- 2 \cdot 1}

数を引く:

- 2 - 2 = - 4

= \frac{- 4}{- 2 \cdot 1}

数を乗じる:

2 \cdot 1 = 2

= \frac{- 4}{- 2}

分数の規則を適用する:

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

= \frac{4}{2}

数を割る:

\frac{4}{2} = 2

= 2

二次equationの解:

u = 0, u = 2

代用を戻す

u = cos (x)

cos (x) = 0, cos (x) = 2

cos (x) = 0, cos (x) = 2

cos (x) = 0 : x = \frac{π}{2} + 2 πn, x = \frac{3 π}{2} + 2 πn

cos (x) = 0

以下の一般解

cos (x) = 0

cos (x)

2 πn

循環を含む周期性テーブル:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} cos (x) 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} cos (x) - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2}

x = \frac{π}{2} + 2 πn, x = \frac{3 π}{2} + 2 πn

x = \frac{π}{2} + 2 πn, x = \frac{3 π}{2} + 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 = \frac{π}{2} + 2 πn, x = \frac{3 π}{2} + 2 πn

グラフ

人気の例

2sin^2(x)+sqrt(2)sin(x)=0

2 sin^{2} (x) + 2 sin (x) = 0

8sin(x)cos(x)=0

8 sin (x) cos (x) = 0

cos (θ) = \frac{9}{41}

cos (x) = \frac{13}{19}

0 = 3 cos (2 x)