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人気のある三角関数 >

2cos^2(x)=sqrt(3)*cos(x)

解

2 cos^{2} (x) = 3 \cdot cos (x)

解

x = \frac{π}{2} + 2 πn, x = \frac{3 π}{2} + 2 πn, x = \frac{π}{6} + 2 πn, x = \frac{11 π}{6} + 2 πn

+1

度

x = 9 0^{\circ} + 36 0^{\circ} n, x = 27 0^{\circ} + 36 0^{\circ} n, x = 3 0^{\circ} + 36 0^{\circ} n, x = 33 0^{\circ} + 36 0^{\circ} n

解答ステップ

2 cos^{2} (x) = 3 cos (x)

置換で解く

2 cos^{2} (x) = 3 cos (x)

仮定:

cos (x) = u

2 u^{2} = 3 u

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

2 u^{2} = 3 u

3 u

を左側に移動します

2 u^{2} = 3 u

両辺から

3 u

を引く

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

簡素化

2 u^{2} - 3 u = 0

2 u^{2} - 3 u = 0

因数

2 u^{2} - 3 u : u (2 u - 3)

2 u^{2} - 3 u

指数の規則を適用する:

a^{b + c} = a^{b} a^{c}

u^{2} = uu

= 2 uu - 3 u

共通項をくくり出す

u

= u (2 u - 1 \cdot 2 3)

数を乗じる:

1 \cdot 2 = 2

= u (2 u - 3)

u (2 u - 3) = 0

零因子の原則を使用:

ab = 0

ならば

a = 0

または

b = 0

u = 0 or 2 u - 3 = 0

解く

2 u - 3 = 0 : u = \frac{3}{2}

2 u - 3 = 0

3

を右側に移動します

2 u - 3 = 0

両辺に

3

を足す

2 u - 3 + 3 = 0 + 3

簡素化

2 u = 3

2 u = 3

以下で両辺を割る

2

2 u = 3

以下で両辺を割る

2

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

簡素化

u = \frac{3}{2}

u = \frac{3}{2}

二次equationの解:

u = 0, u = \frac{3}{2}

代用を戻す

u = cos (x)

cos (x) = 0, cos (x) = \frac{3}{2}

cos (x) = 0, cos (x) = \frac{3}{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) = \frac{3}{2} : x = \frac{π}{6} + 2 πn, x = \frac{11 π}{6} + 2 πn

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

以下の一般解

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

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}{6} + 2 πn, x = \frac{11 π}{6} + 2 πn

x = \frac{π}{6} + 2 πn, x = \frac{11 π}{6} + 2 πn

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, x = \frac{π}{6} + 2 πn, x = \frac{11 π}{6} + 2 πn

グラフ

人気の例

4(cos(x)+1)cos(x)=3

4 (cos (x) + 1) cos (x) = 3

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