Find all the solutions in the interval [−2π, 2π] of the equation cos θ = 0.
pi/2
3 pi/2
and I suppose
-pi/2
-3 pi/2
To find all the solutions in the interval [−2π, 2π] of the equation cos θ = 0, we need to determine the values of θ that satisfy this equation.
First, let's recall the unit circle and the values of cosine at different angles:
```
θ = 0 cos θ = 1
θ = π/2 cos θ = 0
θ = π cos θ = -1
θ = 3π/2 cos θ = 0
θ = 2π cos θ = 1
```
From this, we can see that the values of cosine become zero at angles π/2 and 3π/2.
Since we are looking for solutions in the interval [−2π, 2π], we find that both π/2 and 3π/2 fall within this range. Therefore, the solutions to the equation cos θ = 0 in the interval [−2π, 2π] are θ = π/2 and θ = 3π/2.
In summary, the solutions to the equation cos θ = 0 in the interval [−2π, 2π] are θ = π/2 and θ = 3π/2.