# How do you solve: sin2θ + cosθ = 0 between 0 and 2pi?

##### 3 Answers

#### Explanation:

We're going to want to get rid of the double angle,

Recall the identity

Note that all of these terms involve

We now solve the following equations:

Each coordinate pair

For

We see this holds true for

I tried this:

#### Explanation:

We can write:

so that our equation becomes:

collect:

so, this equation is satisfied either when:

i.e. when

or when:

i.e. when

#### Explanation:

You knew a 30/60/90 or 45/45/90 triangle was going to show up sooner or later.

The last two came from two supplementary angles (

Let's enumerate

From

From

From

Check: I'll check a couple, leave the rest for you.

That's the end, but I'll keep writing so feel free to keep reading this optional part..

Getting those

We rewrite

Applying our solutions,

which is essentially what we got.