00:01
So in this problem, you're being asked to find all the solutions to the given equation on an interval from 0 to 2 pi, meaning if you're thinking about degrees, between 0 and 360 degrees.
00:12
Well, the first thing i notice is i have two different trig functions.
00:15
I have sine and cosine.
00:16
So i want to rewrite them in terms of the same trig function.
00:19
So i'm going to focus on sine squared.
00:21
We're going to use our pythagorean identity that says that sine squared of x plus the cosine squared of x is equal to 1.
00:29
So if i was to isolate sine squared of x, i would subtract cosine squared x from both sides of our equation, which would leave us with the sine squared of x equal to 1 minus the cosine squared of x.
00:40
So now we can substitute 1 minus cosine squared x in place of sine squared x in our equation.
00:45
So we have 1 minus the cosine squared of x equal to 1 minus the cosine of x.
00:51
So now what we're going to do is we're going to set this equation equal to 0.
00:55
To do this, i can subtract 1 from both sides, and at the same time, i can add the cosine squared of x to both sides of our equation...