Question

resolva as equações sen(4x+π/2)= -√2/2

Answer 1

Resposta:

x=3π/16+ kπ/2 ou x= 5π/16 +kπ/2

Explicação passo-a-passo:

Transformando -√2/2 em sen 5π/4:

sen(4x+π/2)= -sen 5π/4

Cortando o seno, temos:

4x+ π/2= 5π/4 +2kπ

Passando π/2:

4x= 5π/4-π/2 +2kπ

somando 5π/4 e -π/2 pelo mmc:

4x=3π/4 +2kπ

Passando o 4:

x= 3π/16 + kπ/2

Sendo -√2/2=sen 7π/4, temos:

sen (4x+π/2)= sen 7π/4

Cortando o seno:

4x+π/2= 7π/4 +2kπ

Passando π/2:

4x= 7π/4-π/2 +2kπ

Diminuindo 7π/4 por π/2:

4x= 5π/4 +2kπ

Passando o 4 dividindo:

x=5π/16 + kπ/2