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.