To solve for x in the equation 1 + 2cos(x) = 0, we need to isolate the cosine term first.
Subtract 1 from both sides:2cos(x) = -1
Divide by 2:cos(x) = -1/2
Now, we need to find the angle whose cosine is -1/2. This angle is arccos(-1/2) or cos^(-1)(-1/2).
Using the unit circle or calculator, we know that cos(π/3) = 1/2 and cos(2π/3) = -1/2.
Therefore, x can be either π/3 or 2π/3.
So, the solutions for x are:x = π/3 or x = 2π/3.
To solve for x in the equation 1 + 2cos(x) = 0, we need to isolate the cosine term first.
Subtract 1 from both sides:
2cos(x) = -1
Divide by 2:
cos(x) = -1/2
Now, we need to find the angle whose cosine is -1/2. This angle is arccos(-1/2) or cos^(-1)(-1/2).
Using the unit circle or calculator, we know that cos(π/3) = 1/2 and cos(2π/3) = -1/2.
Therefore, x can be either π/3 or 2π/3.
So, the solutions for x are:
x = π/3 or x = 2π/3.