Find all solutions to the equation. sin2x + sin x = 0

Answer 1

sin(2x) + sinx = 0

2sinxcosx + sinx = 0

sinx ( 2cosx + 1) = 0

sinx = 0 or cosx = -1/2

sinx = 0 when x = kπ, where k = 0, 1, -1, 2, -2, ...

cosx = -1/2 when x = 2π/3 + 2kπ or 4π/3 + 2kπ

Answer 2

sin² x + sin x = 0

sin x (sin x + 1) = 0

Use the zero-product rule from Algebra 2 to solve.