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人気のある三角関数 >

cos^2(x)= 1/2+1/2 cos^2(x)

解

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

解

x = 2 πn, x = π + 2 πn

+1

度

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

解答ステップ

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

置換で解く

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

仮定:

cos (x) = u

u^{2} = \frac{1}{2} + \frac{1}{2} u^{2}

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

u^{2} = \frac{1}{2} + \frac{1}{2} u^{2}

\frac{1}{2} u^{2}

を左側に移動します

u^{2} = \frac{1}{2} + \frac{1}{2} u^{2}

両辺から

\frac{1}{2} u^{2}

を引く

u^{2} - \frac{1}{2} u^{2} = \frac{1}{2} + \frac{1}{2} u^{2} - \frac{1}{2} u^{2}

簡素化

\frac{1}{2} u^{2} = \frac{1}{2}

\frac{1}{2} u^{2} = \frac{1}{2}

以下で両辺を乗じる:

2

\frac{1}{2} u^{2} = \frac{1}{2}

以下で両辺を乗じる:

2

2 \cdot \frac{1}{2} u^{2} = \frac{1 \cdot 2}{2}

簡素化

2 \cdot \frac{1}{2} u^{2} = \frac{1 \cdot 2}{2}

簡素化

2 \cdot \frac{1}{2} u^{2} : u^{2}

2 \cdot \frac{1}{2} u^{2}

分数を乗じる:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{1 \cdot 2}{2} u^{2}

共通因数を約分する:

2

= u^{2} \cdot 1

乗算:

u^{2} \cdot 1 = u^{2}

= u^{2}

簡素化

\frac{1 \cdot 2}{2} : 1

\frac{1 \cdot 2}{2}

数を乗じる:

1 \cdot 2 = 2

= \frac{2}{2}

規則を適用

\frac{a}{a} = 1

= 1

u^{2} = 1

u^{2} = 1

u^{2} = 1

x^{2} = f (a)

の場合, 解は

x = f (a), - f (a)

u = 1, u = - 1

1 = 1

1

規則を適用

1 = 1

= 1

- 1 = - 1

- 1

規則を適用

1 = 1

= - 1

u = 1, u = - 1

代用を戻す

u = cos (x)

cos (x) = 1, cos (x) = - 1

cos (x) = 1, cos (x) = - 1

cos (x) = 1 : x = 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 = 0 + 2 πn

x = 0 + 2 πn

解く

x = 0 + 2 πn : x = 2 πn

x = 0 + 2 πn

0 + 2 πn = 2 πn

x = 2 πn

x = 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 = 2 πn, x = π + 2 πn

グラフ

人気の例

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