Question

Sin(п+х)=-1/2 на [-2п;0]

Answer 1

Решение прикреплено. Удачи

Answer 2

To solve the equation sin(п + х) = -1/2 on the interval [-2п, 0], we need to find the values of х that satisfy the equation.

The equation sin(п + х) = -1/2 can be rewritten as:

sin(х + п) = -1/2

Now, we know that sin(θ) = -1/2 has solutions at two specific angles in the interval [0, 2п]: π/6 and 5π/6.

To find the values of х in the interval [-2п, 0], we need to shift these angles by π units (as х + π = θ). Let's find these values:

1. For π/6: х + π = π/6 х = π/6 - π х = -5π/6

2. For 5π/6: х + π = 5π/6 х = 5π/6 - π х = -π/6

So, the solutions for х in the interval [-2π, 0] are -5π/6 and -π/6.