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人気のある三角関数 >

4sin^2(x)-1=0,0<= x<2pi

解

4 sin^{2} (x) - 1 = 0, 0 \leq x < 2 π

解

x = \frac{π}{6}, x = \frac{5 π}{6}, x = \frac{7 π}{6}, x = \frac{11 π}{6}

+1

度

x = 3 0^{\circ}, x = 15 0^{\circ}, x = 21 0^{\circ}, x = 33 0^{\circ}

解答ステップ

4 sin^{2} (x) - 1 = 0, 0 \leq x < 2 π

置換で解く

4 sin^{2} (x) - 1 = 0

仮定:

sin (x) = u

4 u^{2} - 1 = 0

4 u^{2} - 1 = 0 : u = \frac{1}{2}, u = - \frac{1}{2}

4 u^{2} - 1 = 0

1

を右側に移動します

4 u^{2} - 1 = 0

両辺に

1

を足す

4 u^{2} - 1 + 1 = 0 + 1

簡素化

4 u^{2} = 1

4 u^{2} = 1

以下で両辺を割る

4

4 u^{2} = 1

以下で両辺を割る

4

\frac{4 u ^{2}}{4} = \frac{1}{4}

簡素化

u^{2} = \frac{1}{4}

u^{2} = \frac{1}{4}

x^{2} = f (a)

の場合, 解は

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

u = \frac{1}{4}, u = - \frac{1}{4}

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

\frac{1}{4}

累乗根の規則を適用する:

, 以下を想定

a \geq 0, b \geq 0

= \frac{1}{4}

4 = 2

4

数を因数に分解する:

4 = 2^{2}

= 2^{2}

累乗根の規則を適用する:

2^{2} = 2

= 2

= \frac{1}{2}

規則を適用

1 = 1

= \frac{1}{2}

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

- \frac{1}{4}

簡素化

\frac{1}{4} : \frac{1}{2}

\frac{1}{4}

累乗根の規則を適用する:

, 以下を想定

a \geq 0, b \geq 0

= \frac{1}{4}

4 = 2

4

数を因数に分解する:

4 = 2^{2}

= 2^{2}

累乗根の規則を適用する:

2^{2} = 2

= 2

= \frac{1}{2}

= - \frac{1}{2}

規則を適用

1 = 1

= - \frac{1}{2}

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

代用を戻す

u = sin (x)

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

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

sin (x) = \frac{1}{2}, 0 \leq x < 2 π : x = \frac{π}{6}, x = \frac{5 π}{6}

sin (x) = \frac{1}{2}, 0 \leq x < 2 π

以下の一般解

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

sin (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} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{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} sin (x) 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2}

x = \frac{π}{6} + 2 πn, x = \frac{5 π}{6} + 2 πn

x = \frac{π}{6} + 2 πn, x = \frac{5 π}{6} + 2 πn

範囲の解答

0 \leq x < 2 π

x = \frac{π}{6}, x = \frac{5 π}{6}

sin (x) = - \frac{1}{2}, 0 \leq x < 2 π : x = \frac{7 π}{6}, x = \frac{11 π}{6}

sin (x) = - \frac{1}{2}, 0 \leq x < 2 π

以下の一般解

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

sin (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} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{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} sin (x) 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2}

x = \frac{7 π}{6} + 2 πn, x = \frac{11 π}{6} + 2 πn

x = \frac{7 π}{6} + 2 πn, x = \frac{11 π}{6} + 2 πn

範囲の解答

0 \leq x < 2 π

x = \frac{7 π}{6}, x = \frac{11 π}{6}

すべての解を組み合わせる

x = \frac{π}{6}, x = \frac{5 π}{6}, x = \frac{7 π}{6}, x = \frac{11 π}{6}

グラフ

人気の例

cos^2(x)-4sin^2(x)=2

2cos(2θ)=sqrt(2)