# How do I find #sintheta# = #-cos^2theta# -1 in radians from #[0, 2pi]#?

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How do I find #sintheta# = #-cos^2theta# -1 in radians from #[0, 2pi]# ?

How do I find

##### 3 Answers

#### Explanation:

Since

(note that

#### Explanation:

We can get this equation in terms of one trigonometric function using trig identities. In this case, we know the identity

So, we apply it to the right side:

Move everything to the right. This gives us the following:

Or,

This strongly resembles a quadratic equation; however, instead of

As a result, we can factor this just as we would factor a quadratic:

We then solve the following:

For

Tells us this one has no solutions, as

Holds true for

#### Explanation:

We can use one of the Pythagorean identities to write our equation in terms of a single trigonometric function. In particular, we can use:

We get:

We'll solve as follows.

The product of the factors

So if the equation has a solution, at least one of the factors must be zero.

or

Sine has the value

It NEVER has the value