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人気のある三角関数 >

2sin^2(x)=sqrt(2)sin(x)

解

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

解

x = 2 πn, x = π + 2 πn, x = \frac{π}{4} + 2 πn, x = \frac{3 π}{4} + 2 πn

+1

度

x = 0^{\circ} + 36 0^{\circ} n, x = 18 0^{\circ} + 36 0^{\circ} n, x = 4 5^{\circ} + 36 0^{\circ} n, x = 13 5^{\circ} + 36 0^{\circ} n

解答ステップ

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

置換で解く

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

仮定:

sin (x) = u

2 u^{2} = 2 u

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

2 u^{2} = 2 u

2 u

を左側に移動します

2 u^{2} = 2 u

両辺から

2 u

を引く

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

簡素化

2 u^{2} - 2 u = 0

2 u^{2} - 2 u = 0

因数

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

2 u^{2} - 2 u

指数の規則を適用する:

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

u^{2} = uu

= 2 uu - 2 u

共通項をくくり出す

u

= u (2 u - 1 \cdot 2 1 \cdot 2)

数を乗じる:

1 \cdot 2 = 2

= u (2 u - 2)

u (2 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 2 u - 2 = 0

解く

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

2 u - 2 = 0

2

を右側に移動します

2 u - 2 = 0

両辺に

2

を足す

2 u - 2 + 2 = 0 + 2

簡素化

2 u = 2

2 u = 2

以下で両辺を割る

2

2 u = 2

以下で両辺を割る

2

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

簡素化

u = \frac{2}{2}

u = \frac{2}{2}

二次equationの解:

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

代用を戻す

u = sin (x)

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

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

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}{2} : x = \frac{π}{4} + 2 πn, x = \frac{3 π}{4} + 2 πn

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

以下の一般解

sin (x) = \frac{2}{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}{4} + 2 πn, x = \frac{3 π}{4} + 2 πn

x = \frac{π}{4} + 2 πn, x = \frac{3 π}{4} + 2 πn

すべての解を組み合わせる

x = 2 πn, x = π + 2 πn, x = \frac{π}{4} + 2 πn, x = \frac{3 π}{4} + 2 πn

グラフ

人気の例

cos(2x)+3sin(x)-2=0

cos (2 x) + 3 sin (x) - 2 = 0

tan (a) = 3

tan (x) = \frac{6}{8}

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

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

cos(x)tan^2(x)=cos(x)

cos (x) tan^{2} (x) = cos (x)