00:02
Okay, so i'm given that the sign of x is 7 over 9 and x is in quadrant 1.
00:10
Okay, so i'm going to draw this angle.
00:13
Sign is opposite over hypotenuse.
00:17
I'm going to use pythagorean theorem to get that missing side.
00:23
So that's 49 and 81.
00:28
Subtract 49 from both sides.
00:33
I'm going to get a square.
00:35
Is 32, so a is the square root of 32, which is just 16 times 2, so that's 4 radical 2.
00:50
Okay.
00:52
Now, i've got the sign.
00:55
I'm going to want cosine, so cosine is 4 radical 2 over 9, and i want tangent.
01:03
Tangent is opposite over a g cent.
01:10
Okay.
01:11
Now, i want to find sine 2x.
01:16
So that's 2 times the sine times the cosine.
01:22
So that's 2 times 7 over 9 times 4 red 2 over 9.
01:34
So that's going to give me, let's see, 2 times 2 times.
01:39
Times 2 times 7 times 4 is 56, radical 2 over 81.
01:54
There's my cosine, my sine 2x.
01:58
For cosine 2x, i'm going to use, i have three different rules that i can choose from.
02:04
I'm going to use 1 minus 2 sine squared x.
02:09
So that's 7 over 9, and i'm going to square...