Question #6192d

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Answer 1 · 2017-06-02T19:45:34

$θ = π \pm π n$ $theta = pi pm pi n$ ; $n in ZZ$

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.

enter image source here

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:

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