00:01
So in this problem, we're told that theta is going to be in the cute angle, so first quadrant, and we know that the tangent of theta is equal to x.
00:07
So we want to represent the upper five trig functions in terms of x.
00:11
Well, let's start by drawing this.
00:13
So we know this angle is in the first quadrant.
00:15
So if we draw our reference triangle here, this would be our angle for x.
00:19
Or sorry, our angle of theta, not x.
00:21
All right.
00:22
Well, let's think about what we know about the tangent function.
00:25
Well, it's equal to the ratio of the opposite side over the adjacent side.
00:29
Well, if i was to take x and write it as a fraction, it would be x over 1.
00:32
So the opposite side would be x and the adjacent side would be 1.
00:36
So now what we're going to do is writing an expression for the hypotenuse in terms of x.
00:41
So for right now, i'm going to call it y.
00:42
So to do this, we're going to use the pythagorean theorem.
00:45
So we're going to have x squared plus 1 squared equal to y squared.
00:48
Well, one squared is just one.
00:51
So in order to get y by itself, all we're going to do is take the square root of both sides.
00:55
So we're going to have the square root of x squared plus 1 equal to y.
01:00
Perfect.
01:01
So now we can go back to our diagram...