How do you solve: sin2θ + cosθ = 0 between 0 and 2pi?
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
We see this holds true for
I tried this:
We can write:
so that our equation becomes:
so, this equation is satisfied either when:
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 (
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..
Applying our solutions,
which is essentially what we got.