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人気のある三角関数 >

5sin^2(x)=2sin(x)

解

5 sin^{2} (x) = 2 sin (x)

解

x = 2 πn, x = π + 2 πn, x = 0.41151 \dots + 2 πn, x = π - 0.41151 \dots + 2 πn

+1

度

x = 0^{\circ} + 36 0^{\circ} n, x = 18 0^{\circ} + 36 0^{\circ} n, x = 23.57817 \dots^{\circ} + 36 0^{\circ} n, x = 156.42182 \dots^{\circ} + 36 0^{\circ} n

解答ステップ

5 sin^{2} (x) = 2 sin (x)

置換で解く

5 sin^{2} (x) = 2 sin (x)

仮定:

sin (x) = u

5 u^{2} = 2 u

5 u^{2} = 2 u : u = 0, u = \frac{2}{5}

5 u^{2} = 2 u

2 u

を左側に移動します

5 u^{2} = 2 u

両辺から

2 u

を引く

5 u^{2} - 2 u = 2 u - 2 u

簡素化

5 u^{2} - 2 u = 0

5 u^{2} - 2 u = 0

因数

5 u^{2} - 2 u : u (5 u - 2)

5 u^{2} - 2 u

指数の規則を適用する:

a^{b + c} = a^{b} a^{c}

u^{2} = uu

= 5 uu - 2 u

共通項をくくり出す

u

= u (5 u - 2)

u (5 u - 2) = 0

零因子の原則を使用:

ab = 0

ならば

a = 0

または

b = 0

u = 0 or 5 u - 2 = 0

解く

5 u - 2 = 0 : u = \frac{2}{5}

5 u - 2 = 0

2

を右側に移動します

5 u - 2 = 0

両辺に

2

を足す

5 u - 2 + 2 = 0 + 2

簡素化

5 u = 2

5 u = 2

以下で両辺を割る

5

5 u = 2

以下で両辺を割る

5

\frac{5 u}{5} = \frac{2}{5}

簡素化

u = \frac{2}{5}

u = \frac{2}{5}

二次equationの解:

u = 0, u = \frac{2}{5}

代用を戻す

u = sin (x)

sin (x) = 0, sin (x) = \frac{2}{5}

sin (x) = 0, sin (x) = \frac{2}{5}

sin (x) = 0 : x = 2 πn, x = π + 2 πn

sin (x) = 0

以下の一般解

sin (x) = 0

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 = 0 + 2 πn, x = π + 2 πn

x = 0 + 2 πn, x = π + 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, x = π + 2 πn

sin (x) = \frac{2}{5} : x = arcsin (\frac{2}{5}) + 2 πn, x = π - arcsin (\frac{2}{5}) + 2 πn

sin (x) = \frac{2}{5}

三角関数の逆数プロパティを適用する

sin (x) = \frac{2}{5}

以下の一般解

sin (x) = \frac{2}{5}

sin (x) = a \Rightarrow x = arcsin (a) + 2 πn, x = π - arcsin (a) + 2 πn

x = arcsin (\frac{2}{5}) + 2 πn, x = π - arcsin (\frac{2}{5}) + 2 πn

x = arcsin (\frac{2}{5}) + 2 πn, x = π - arcsin (\frac{2}{5}) + 2 πn

すべての解を組み合わせる

x = 2 πn, x = π + 2 πn, x = arcsin (\frac{2}{5}) + 2 πn, x = π - arcsin (\frac{2}{5}) + 2 πn

10進法形式で解を証明する

x = 2 πn, x = π + 2 πn, x = 0.41151 \dots + 2 πn, x = π - 0.41151 \dots + 2 πn

グラフ

人気の例

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