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人気のある三角関数 >

2sin(x)cos(x)+sqrt(2)sin(x)=0,0<= x<2pi

解

2 sin (x) cos (x) + 2 sin (x) = 0, 0 \leq x < 2 π

解

x = 0, x = π, x = \frac{3 π}{4}, x = \frac{5 π}{4}

+1

度

x = 0^{\circ}, x = 18 0^{\circ}, x = 13 5^{\circ}, x = 22 5^{\circ}

解答ステップ

2 sin (x) cos (x) + 2 sin (x) = 0, 0 \leq x < 2 π

因数

2 sin (x) cos (x) + 2 sin (x) : sin (x) (2 cos (x) + 2)

2 sin (x) cos (x) + 2 sin (x)

共通項をくくり出す

sin (x)

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

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

各部分を別個に解く

sin (x) = 0 or 2 cos (x) + 2 = 0

sin (x) = 0, 0 \leq x < 2 π : x = 0, x = π

sin (x) = 0, 0 \leq x < 2 π

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

範囲の解答

0 \leq x < 2 π

x = 0, x = π

2 cos (x) + 2 = 0, 0 \leq x < 2 π : x = \frac{3 π}{4}, x = \frac{5 π}{4}

2 cos (x) + 2 = 0, 0 \leq x < 2 π

2

を右側に移動します

2 cos (x) + 2 = 0

両辺から

2

を引く

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

簡素化

2 cos (x) = - 2

2 cos (x) = - 2

以下で両辺を割る

2

2 cos (x) = - 2

以下で両辺を割る

2

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

簡素化

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

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

以下の一般解

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

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}

x = \frac{3 π}{4} + 2 πn, x = \frac{5 π}{4} + 2 πn

x = \frac{3 π}{4} + 2 πn, x = \frac{5 π}{4} + 2 πn

範囲の解答

0 \leq x < 2 π

x = \frac{3 π}{4}, x = \frac{5 π}{4}

すべての解を組み合わせる

x = 0, x = π, x = \frac{3 π}{4}, x = \frac{5 π}{4}

グラフ

人気の例

(cos (x) + 1) = 0

3cos(2θ)-5cos(θ)=1

3 cos (2 θ) - 5 cos (θ) = 1

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

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

cot(θ/3+(3pi)/4)=sqrt(3)

cot (\frac{θ}{3} + \frac{3 π}{4}) = 3

cos(x)=(tan(x)+cot(x))/(csc(x))

cos (x) = \frac{tan ( x ) + cot ( x )}{csc ( x )}