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人気のある三角関数 >

cos^2(x/2)=1

解

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

解

x = 4 πn, x = 2 π + 4 πn

+1

度

x = 0^{\circ} + 72 0^{\circ} n, x = 36 0^{\circ} + 72 0^{\circ} n

解答ステップ

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

置換で解く

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

仮定:

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

u^{2} = 1

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

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

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

cos (\frac{x}{2}) = 1 : x = 4 πn

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

以下の一般解

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

\frac{x}{2} = 0 + 2 πn

\frac{x}{2} = 0 + 2 πn

解く

\frac{x}{2} = 0 + 2 πn : x = 4 πn

\frac{x}{2} = 0 + 2 πn

0 + 2 πn = 2 πn

\frac{x}{2} = 2 πn

以下で両辺を乗じる:

2

\frac{x}{2} = 2 πn

以下で両辺を乗じる:

2

\frac{2 x}{2} = 2 \cdot 2 πn

簡素化

x = 4 πn

x = 4 πn

x = 4 πn

cos (\frac{x}{2}) = - 1 : x = 2 π + 4 πn

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

以下の一般解

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

\frac{x}{2} = π + 2 πn

\frac{x}{2} = π + 2 πn

解く

\frac{x}{2} = π + 2 πn : x = 2 π + 4 πn

\frac{x}{2} = π + 2 πn

以下で両辺を乗じる:

2

\frac{x}{2} = π + 2 πn

以下で両辺を乗じる:

2

\frac{2 x}{2} = 2 π + 2 \cdot 2 πn

簡素化

x = 2 π + 4 πn

x = 2 π + 4 πn

x = 2 π + 4 πn

すべての解を組み合わせる

x = 4 πn, x = 2 π + 4 πn

グラフ

人気の例

sin(x)+cos(x)=(sqrt(2))/2

sin (x) + cos (x) = \frac{2}{2}

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