Question

What does it mean to find the value of `theta` that is a solution of the equation `4sin^3(2theta)=-1`?

Answer 1

Here's what it means...(and the answer is `theta = -19.5^@`)

Explanation:

Treat the trigonometry function like any other variable, because that's what it is. We must perform a series of inverse operations - cube root and inverse sine to undo all these operations:

`4sin^3(2theta)=-1`

`sin^3(2theta)=-1/4`

Cube root of both sides:

`sin(2theta)=root(3)(-1/4)`

`sin(2theta)=-1/root(3)(4)`

Inverse sign

`2theta=sin^(-1)(-1/root(3)(4))`

The argument on the right is equal to `-39^@`

So, the final step is to divide both sides by `2`:

`theta =-19.5^@`