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sin(θ)sin(2θ)=0,0<= θ<= 2pi

Solução

sin (θ) sin (2 θ) = 0, 0 \leq θ \leq 2 π

θ = 0, θ = π, θ = 2 π, θ = \frac{π}{2}, θ = \frac{3 π}{2}

Graus

θ = 0^{\circ}, θ = 18 0^{\circ}, θ = 36 0^{\circ}, θ = 9 0^{\circ}, θ = 27 0^{\circ}

Passos da solução

sin (θ) sin (2 θ) = 0, 0 \leq θ \leq 2 π

Resolver cada parte separadamente

sin (θ) = 0 or sin (2 θ) = 0

sin (θ) = 0, 0 \leq θ \leq 2 π : θ = 0, θ = π, θ = 2 π

sin (θ) = 0, 0 \leq θ \leq 2 π

Soluções gerais para

sin (θ) = 0

sin (x)

tabela de periodicidade com ciclo de

2 πn

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 = 0 + 2 πn, θ = π + 2 πn

θ = 0 + 2 πn, θ = π + 2 πn

Resolver

θ = 0 + 2 πn : θ = 2 πn

θ = 0 + 2 πn

0 + 2 πn = 2 πn

θ = 2 πn

θ = 2 πn, θ = π + 2 πn

Soluções para o intervalo

0 \leq θ \leq 2 π

θ = 0, θ = π, θ = 2 π

sin (2 θ) = 0, 0 \leq θ \leq 2 π : θ = 0, θ = \frac{π}{2}, θ = π, θ = \frac{3 π}{2}, θ = 2 π

sin (2 θ) = 0, 0 \leq θ \leq 2 π

Soluções gerais para

sin (2 θ) = 0

sin (x)

tabela de periodicidade com ciclo de

2 πn

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}

2 θ = 0 + 2 πn, 2 θ = π + 2 πn

2 θ = 0 + 2 πn, 2 θ = π + 2 πn

Resolver

2 θ = 0 + 2 πn : θ = πn

2 θ = 0 + 2 πn

0 + 2 πn = 2 πn

2 θ = 2 πn

Dividir ambos os lados por

2

2 θ = 2 πn

Dividir ambos os lados por

2

\frac{2 θ}{2} = \frac{2 πn}{2}

Simplificar

θ = πn

θ = πn

Resolver

2 θ = π + 2 πn : θ = \frac{π}{2} + πn

2 θ = π + 2 πn

Dividir ambos os lados por

2

2 θ = π + 2 πn

Dividir ambos os lados por

2

\frac{2 θ}{2} = \frac{π}{2} + \frac{2 πn}{2}

Simplificar

θ = \frac{π}{2} + πn

θ = \frac{π}{2} + πn

θ = πn, θ = \frac{π}{2} + πn

Soluções para o intervalo

0 \leq θ \leq 2 π

θ = 0, θ = \frac{π}{2}, θ = π, θ = \frac{3 π}{2}, θ = 2 π

Combinar toda as soluções

θ = 0, θ = π, θ = 2 π, θ = \frac{π}{2}, θ = \frac{3 π}{2}

csc (4 x) - 2 = 0

cos (x) = - 0.7

tan^{2} (θ) - tan (θ) = 0

cos (8 0^{\circ})

3 tan (θ) - 1 = 0