sin(θ)=-(sqrt(2))/2 ,0<= θ<2pi

解

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

θ = \frac{5 π}{4}, θ = \frac{7 π}{4}

度

θ = 22 5^{\circ}, θ = 31 5^{\circ}

解答ステップ

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

以下の一般解

sin (θ) = - \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}

θ = \frac{5 π}{4} + 2 πn, θ = \frac{7 π}{4} + 2 πn

θ = \frac{5 π}{4} + 2 πn, θ = \frac{7 π}{4} + 2 πn

範囲の解答

0 \leq θ < 2 π

θ = \frac{5 π}{4}, θ = \frac{7 π}{4}