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人気のある三角関数 >

6cos^2(x)+3cos(x)-3=0

解

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

解

x = \frac{π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn, x = π + 2 πn

+1

度

x = 6 0^{\circ} + 36 0^{\circ} n, x = 30 0^{\circ} + 36 0^{\circ} n, x = 18 0^{\circ} + 36 0^{\circ} n

解答ステップ

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

置換で解く

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

仮定:

cos (x) = u

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

6 u^{2} + 3 u - 3 = 0 : u = \frac{1}{2}, u = - 1

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

解くとthe二次式

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

二次Equationの公式:

次の場合:

a = 6, b = 3, c = - 3

u_{1, 2} = \frac{- 3 \pm 3 ^{2} - 4 \cdot 6 ( - 3 )}{2 \cdot 6}

u_{1, 2} = \frac{- 3 \pm 3 ^{2} - 4 \cdot 6 ( - 3 )}{2 \cdot 6}

3^{2} - 4 \cdot 6 (- 3) = 9

3^{2} - 4 \cdot 6 (- 3)

規則を適用

- (- a) = a

= 3^{2} + 4 \cdot 6 \cdot 3

数を乗じる:

4 \cdot 6 \cdot 3 = 72

= 3^{2} + 72

3^{2} = 9

= 9 + 72

数を足す:

9 + 72 = 81

= 81

数を因数に分解する:

81 = 9^{2}

= 9^{2}

累乗根の規則を適用する:

n a^{n} = a

9^{2} = 9

= 9

u_{1, 2} = \frac{- 3 \pm 9}{2 \cdot 6}

解を分離する

u_{1} = \frac{- 3 + 9}{2 \cdot 6}, u_{2} = \frac{- 3 - 9}{2 \cdot 6}

u = \frac{- 3 + 9}{2 \cdot 6} : \frac{1}{2}

\frac{- 3 + 9}{2 \cdot 6}

数を足す/引く:

- 3 + 9 = 6

= \frac{6}{2 \cdot 6}

数を乗じる:

2 \cdot 6 = 12

= \frac{6}{12}

共通因数を約分する:

6

= \frac{1}{2}

u = \frac{- 3 - 9}{2 \cdot 6} : - 1

\frac{- 3 - 9}{2 \cdot 6}

数を引く:

- 3 - 9 = - 12

= \frac{- 12}{2 \cdot 6}

数を乗じる:

2 \cdot 6 = 12

= \frac{- 12}{12}

分数の規則を適用する:

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

= - \frac{12}{12}

規則を適用

\frac{a}{a} = 1

= - 1

二次equationの解:

u = \frac{1}{2}, u = - 1

代用を戻す

u = cos (x)

cos (x) = \frac{1}{2}, cos (x) = - 1

cos (x) = \frac{1}{2}, cos (x) = - 1

cos (x) = \frac{1}{2} : x = \frac{π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn

cos (x) = \frac{1}{2}

以下の一般解

cos (x) = \frac{1}{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}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn

x = \frac{π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn

cos (x) = - 1 : x = π + 2 πn

cos (x) = - 1

以下の一般解

cos (x) = - 1

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 = π + 2 πn

x = π + 2 πn

すべての解を組み合わせる

x = \frac{π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn, x = π + 2 πn

グラフ

人気の例

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0 = cos (x) + sin (x)

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8 sec (x) + 8 tan (x) = 8

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