Question

WILL MARK BRAINLIEST!!!!!!!!!! Find all solutions to the equation. sin2x + sin x = 0

Answer 1

Answer:

{0, π, 3π/2} +2kπ . . . . for any integer k

Step-by-step explanation:

The equation can be factored as ...

... sin(x)·(sin(x) +1) = 0

This will have solutions where the factors are zero, that is, where sin(x) = 0, and where sin(x) = -1. Those angles are ...

... x ∈ {0, π, 3π/2} + 2kπ . . . . . for k = any integer

Answer 2

Answer:  x = 0π, π, $\frac{3\pi}{2}$

Step-by-step explanation:

sin²x + sinx = 0

First, factor to get: sinx(sinx + 1) = 0

Next, set each factor equal to zero and solve:

sin x = 0

sin x + 1 = 0   ⇒   sin x = -1

Then, look at the Unit Circle to see when those occur:

sin = 0 at: 0π and π

sin = -1 at: $\frac{3\pi}{2}$

x = 0π, π, $\frac{3\pi}{2}$