Question

Question #6192d

Answer 1

`theta = pi pm pi n`; `n in ZZ`

Explanation:

I'm assuming you mean to solve `(sin^(2)(theta))^(2) = 0`.

`Rightarrow (sin^(2)(theta))^(2) = 0`

`Rightarrow sin^(2)(theta) = 0`

`Rightarrow sin(theta) = 0`

Now, let's take a look at the graph of `y = sin(theta)`:

graph{sin(x) [-10, 10, -5, 5]}

The `x`-axis is the axis for all values of `theta`.

We are looking for the values of `theta` for which `sin(theta) = 0`.

On the graph, we can see that `y = 0` for multiple values of `theta`, so there will be multiple solutions to the equation `sin(theta) = 0`.

Also, you haven't specified a domain, so the solutions can be positive or negative.

The coordinates of some of the solutions are shown in the graph above.

The solutions are all multiples of `pi`, i.e. `theta = pi pm pi n` for some integer `n`.

Let's express the solutions formally:

`therefore theta = pi pm pi n`; `n in ZZ`