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人気のある三角関数 >

4sin^2(x)=3,0<= x<= 180

解

4 sin^{2} (x) = 3, 0 \leq x \leq 18 0^{\circ}

解

x = 6 0^{\circ}, x = 12 0^{\circ}

+1

ラジアン

x = \frac{π}{3}, x = \frac{2 π}{3}

解答ステップ

4 sin^{2} (x) = 3, 0 \leq x \leq 18 0^{\circ}

置換で解く

4 sin^{2} (x) = 3

仮定:

sin (x) = u

4 u^{2} = 3

4 u^{2} = 3 : u = \frac{3}{2}, u = - \frac{3}{2}

4 u^{2} = 3

以下で両辺を割る

4

4 u^{2} = 3

以下で両辺を割る

4

\frac{4 u ^{2}}{4} = \frac{3}{4}

簡素化

u^{2} = \frac{3}{4}

u^{2} = \frac{3}{4}

x^{2} = f (a)

の場合, 解は

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

u = \frac{3}{4}, u = - \frac{3}{4}

\frac{3}{4} = \frac{3}{2}

\frac{3}{4}

累乗根の規則を適用する:

n \frac{a}{b} = \frac{n a}{n b},

, 以下を想定

a \geq 0, b \geq 0

= \frac{3}{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:

n a^{n} = a

2^{2} = 2

= 2

= \frac{3}{2}

- \frac{3}{4} = - \frac{3}{2}

- \frac{3}{4}

簡素化

\frac{3}{4} : \frac{3}{2}

\frac{3}{4}

累乗根の規則を適用する:

n \frac{a}{b} = \frac{n a}{n b},

, 以下を想定

a \geq 0, b \geq 0

= \frac{3}{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:

n a^{n} = a

2^{2} = 2

= 2

= \frac{3}{2}

= - \frac{3}{2}

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

代用を戻す

u = sin (x)

sin (x) = \frac{3}{2}, sin (x) = - \frac{3}{2}

sin (x) = \frac{3}{2}, sin (x) = - \frac{3}{2}

sin (x) = \frac{3}{2}, 0 \leq x \leq 18 0^{\circ} : x = 6 0^{\circ}, x = 12 0^{\circ}

sin (x) = \frac{3}{2}, 0 \leq x \leq 18 0^{\circ}

以下の一般解

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

sin (x)

36 0^{\circ} n

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 = 6 0^{\circ} + 36 0^{\circ} n, x = 12 0^{\circ} + 36 0^{\circ} n

x = 6 0^{\circ} + 36 0^{\circ} n, x = 12 0^{\circ} + 36 0^{\circ} n

範囲の解答

0 \leq x \leq 18 0^{\circ}

x = 6 0^{\circ}, x = 12 0^{\circ}

sin (x) = - \frac{3}{2}, 0 \leq x \leq 18 0^{\circ} :

解なし

sin (x) = - \frac{3}{2}, 0 \leq x \leq 18 0^{\circ}

以下の一般解

sin (x) = - \frac{3}{2}

sin (x)

36 0^{\circ} n

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 = 24 0^{\circ} + 36 0^{\circ} n, x = 30 0^{\circ} + 36 0^{\circ} n

x = 24 0^{\circ} + 36 0^{\circ} n, x = 30 0^{\circ} + 36 0^{\circ} n

範囲の解答

0 \leq x \leq 18 0^{\circ}

解なし

すべての解を組み合わせる

x = 6 0^{\circ}, x = 12 0^{\circ}

グラフ

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