Question

Which of the following are general solutions to the given equation?

sin (7/2)x=(√3)/2
Select all that are true. If there are none that are true, do no select any before submitting.

x=11π/21+(4n/7)π
x=12π/21+(4n/7)π
x=π/21+(4n/7)π
x=4π/21+(4n/7)π
x=π/3+(4n/7)π
x=8π/21+(4n/7)π
x=π/2+(4n/7)π
x=π/14+(4n/7)π

my answer is none of the above
can you double check please...thanks

Answer 1

since the period of sin(kx) = 2π/k, we need

2π/k = 7/2
k = 4π/7

sin (7/2 x) = (√3)/2
7/2 x = π/3, 2π/3
x = 2π/21, 4π/21 + 4nπ/7