00:01
Okay, so we're given sign of x, that's equal to 5 over 12, and we're given that it's in quadrant 1, and we're asked to find sine of 2x, cosine of 2x, and tangent of 2x.
00:10
So i've written out our formulas here, and notice that for tangent of 2x, i didn't use our double angle formulas.
00:19
Instead, i just used the definition of tangent, which is sine over cosine.
00:27
In this case, we have sine of 2x over cosine of 2x, well, that's these two terms here.
00:32
Okay, so let's begin.
00:35
We have 2 sine of x, that's 5 over 12.
00:41
Okay, and now we need to find cosine of x.
00:44
We'll note that if we have sine of x is equal to 5 over 12, that's opposite over hypotenuse.
00:53
So we need to solve for this term here.
00:55
So that's, we know 5 squared plus question mark squared is equal to 12 squared.
01:03
So we get question mark squared is equal to 12 squared.
01:05
To 12 squared minus 5 squared, so that's 144 minus 25, which is 119.
01:13
And then the square root of that, that's equal to, we'll just leave it as so.
01:26
And we'll take the positive square root since we're in quadrant 1, which has both our x and our y value as positive.
01:37
Okay, so we have then cosine of x...