00:01
In this question, we're asked to evaluate this equation to find values of theta that make this equation true.
00:08
And we're looking at angles between zero and up to, but not including, 2 pi.
00:14
So the first thing i'm going to do is just put both trig functions on the same side.
00:19
So i'm going to subtract over the tangent theta.
00:23
So actually we'll write it like this.
00:28
Siquant theta minus tangent theta.
00:33
Equals root 3.
00:35
Now, we know that we're looking for something with root 3s.
00:39
So the two angles that should come to mind are pi over 3 and pi over 6.
00:50
And we'll just whip out the sides real quick.
00:57
Okay, so here, in order to get a root 3 so easily, we most likely want values of secant and tangent that involve our root 3.
01:10
So if we look over here, a secant of pi over 3 would actually be 2.
01:18
So that's probably not what we want.
01:21
And that says we want pi over 6 or some variation thereof that gives us a root 3.
01:31
So root 3.
01:35
Now if we had just sicken of pi over 6, we can see this, 2 over root 3, which is the same as 2 root 3 over 3.
01:49
And tangent of pi over 6 would be opposite over adjacent, 1 over 3, just same as root 3 over 3.
02:04
Now, when we look at this, we notice that if we were to just have pi over 6, we would have 2 root 3 over 3, minus root 3 over 3...