00:01
A good start to this problem would be to identify that if cosine is positive 28 over 53, and the fact that sign is positive, that's what that next statement is, then you're definitely in quadrant one.
00:22
That's poorly drawn, but not a big deal.
00:25
But the other thing that's important is if you made a right triangle in here, just a pretty lame triangle, just drawing it in here, that cosine is adjacent over hypotenuse.
00:39
At least this is how i like to do the problem.
00:41
Adjacent to theta would be 28 is on the x -axis, and the 53 is the hypotenuse.
00:48
Now, there's other ways of doing this, but what i would do is just the pythagorean theorem, called this side y, that 28 squared plus y squared is equal to 53 squared.
01:00
And then you can, i'm just going to go to a calculator because i don't know if this is an easy number.
01:07
That 53 squared minus 28 squared is 2025, which my gut is telling me is a perfect square number that i had no idea about.
01:21
It's 45.
01:22
Look at that.
01:23
You square root both sides.
01:25
And that value is 45.
01:27
Now remember, if it's sokatoa, sign is opposite over hypotenuse.
01:33
So now that we know the opposite is 45, and the hypotenuse is still 53.
01:39
So why did i need to do that? well, if i asked you to do sign of 2 theta, the formula, and it's just a quick internet search, is 2, sine theta, cosine theta.
01:51
So as you're looking at that then, 2 times sine of theta being 45 over 53, and cosine being 28 over 53 just make sure you do two times 45 times 28 that goes in the numerator is 2520 i don't even know if you're allowed to use a calculator and then 53 times 53 and the denominator is 2809 and i'm going to sort of cheat and use my calculator to simplify it does not simplify so 2520 over 2809 is the best answer there now there's a lot of different ways you could do cosine, but what i would actually do, because this is just how my brain works, i would just use a formula that only uses cosine...