Shadow Ninja Doesn't Understand Math/Please Help Me Thread

[Shadow Ninja 2.0]

So, I've got a problem I need to solve rather soon. It's a trigonometric equation, and for the life of me I can't figure it out.

The equation is: sinθ - cosθ = 1

So, what I've done is squared both sides, ending up with sin^2θ - 2cosθsinθ + cos^2θ = 1
Then I reduced that using the Pythagorean identity to get: 1 - 2cosθsinθ = 1
Then I subtracted the one, giving me: -2cosθsinθ = 0
And that can be changed using the double angle formula to get: -cos2θ = 0


This is where I get lost. I understand I'm supposed to find where cos equals 0, but then what? I think I'd get -pi/2, and then divide that by two, and get -pi/4.

What I'm confused about is my teacher said something about because of the way we write it, it'll come out like -pi/4 + pi/2k.

Does anyone know this, and could you help me? I would be very grateful.

[Tom Bombadil]

Trig is stupid. Skip it.

[Shadow Ninja 2.0]

Unfortunately, that is not an option.

[Tom Bombadil]

Haha yeah sorry, I honestly have no idea how to do that. The only trig identity I've ever used outside of trig class is Sin^2x + Cos^2 x = 1

So basically, if you don't get it, you might be screwed for your next test, but in the long run you really won't need it. Unfortunately I can't help any more than that

[Shadow Ninja 2.0]

I really need to ace this test though, otherwise my grade will be in deep doo-doo.

[Zook]

I really need to ace this test though, otherwise my grade will be in deep doo-doo.

[wolfking]

That episode was awesome.

[Shadow Ninja 2.0]

I know there are math people here somewhere. Show yourselves.














plz

[Tom Bombadil]

Alright well after putting my mind to it this is my explanation then...

Ok well assuming you did everything right up to the -cos2θ=0 (which looks good to me, but I don't know my identities), then when you solve for θ you would get -pi/4, since cos goes to 0 at pi/2, so divide that by 2 and you get -pi/4.

All the +pi/2k means is that it will repeat every pi/2k, where k is any integer (so the answer is -pi/4, -3pi/4, -5pi/4, and so on). Since the cosine wave repeats every 2pi, the answer -pi/4 will appear in an infinite number of locations unless you are specified an interval (usually [-2pi, 2pi])

So basically you did all the hard stuff you just had to solve for θ and then add the pi/2k to include every repitition.

Hopefully that makes a bit of sense, If not I can try to explain better if needed.

[Shadow Ninja 2.0]

Thanks for the explanation! Although, I realized I was being stupid before, and just substituted angles into the original equation to find the ones that matched. 

[Onno]

Ah, too bad I missed this, I love math. I was asleep though, it was a bit too late for me

[Shadow Ninja 2.0]

Well, I may have more problems soon. Stay tuned.

[Onno]

I'm really tired, going to bed now... But I'd love to help at a more reasonable time of the day