Ok I need some help on a few trig problems. I have to establish the trig functions by making the left side match the right side using trig identities and I can't figure a few of them out.

(sinx+cosx)²+(sinx-cosx)²=2

1- (sin²x / 1+cosx)=cosx


Have to go eat, I'll finish adding the others in later.

The first one is just some foiling and you'll get a very obvious trig identity.

The second one looks familiar, but it's been too long since I've brushed up on my trig identities.

got it

sin²x = 1 - cos²x

1- cos²x = (1 - cosx)(1 + cosx)

(1 - cosx)(1 + cosx) / (1+ cosx) = 1 - cosx

1 - (1 - cosx) = 1 - 1 + cosx = cosx

First one is simple, as you know, sin²x + cos²x = 1. So distribute the exponent and you have your answer.

I thought that you had to foil on that one, just wanted to make sure.

And you can't mess with the right side of the equation. Everything has to be done on the left side. That's why it's bugging me out so much.


You can't distribute when there's addition. And if that were the case then the second equation would be (sin²x-cos²x) which isn't a trig identity.

I thought and still think elementary and secondary/high school overcomplicated trigonometry and made it seem worse than it is.

Really, all these "magical" identities and equation nonsense is actually really simple, especially when you find out how simple sine and cosine are (well, for a secondary level).

I would recommend getting a decent book that actually explains it. An example would be one that actually starts with "the unit circle," i.e. a circle with radius 1, and moves on from there. Of course, there's more to it, but something like that really helps, in my opinion; instead of memorizing all that nonsense, you will be able to easily derive them in minutes.

An example would be the book "Calculus with anolytic Geometry," by George F. Simmons. This book in particular isn't that great, but it has some features I appreciate, such as the Section 9.1 of Chapter 9 that talks about what I am talking about (you don't need to know any calculus at all, its just a section to review trigonometry).

I know the entire unit circle by heart, and I know most all of the identities by heart and how they correlate. I can work out most of them it's just the ones that you have to take a back way in to figure out that mess with me. Until last week I was doing fine, then something just hit and now I can't do them at all.

I'm guessing that I was completely distracted earlier when I replied to this, because even I can see my answer makes no damn sense.

Haha it's ok. I do the same thing in class. I'll sit there for 10 minutes arguing that my way is right then I look up and

All my work is on the left side. I just drew equal signs to show my work better. Basically I broke it down into the individual steps you would go through. Sin²x = 1 - cos²x is the identity I used, then I just broke it down from there.

basically it was:

1. Identity

2. Unfoil

3. division

4. distributive property and basic subtraction.

Ahh I see it now, I was looking at it wrong. Thanks man.

Oh, sorry! I didn't mean to say that you didn't understand it. I just meant to give my opinion on trigonometry and the identities

Yea, I remember spending a lot of time on these,

Oh haha

Yeah my teacher made us take a mastery test on the unit circle. Had to solve a bunch of trig problems without being able to look at it. Miss one and you fail. Needless to say that's the one thing I actually studied for in that class haha

Oh my goodness....my head hurts. Well thats why I am a Secondary Social Science major and not math I stopped with college algebra

D=

I am glad to say I've never encountered a test like that before

Yeah, she started it a month ago and people are still taking retakes. What's sad is there's only 16 people in my class. So after a month only about 6 people have passed it.

Add them together and then carry the one. I'm in the Mensa society.

Lol Jk.

ouch,

I don't quite understand why she would want to grade her student's ability by a test like that... I can't see the consequent marks reflecting very well the material learned and understood by the students,

That whole class is ridiculously hard. All the tests are 10 questions long and 80% of your grade is your tests, 20% is homework which is also 10 questions. So your homework wont help you if you bomb a test but if you don't do it, the best you can get is an 80/B with 100/A's on all your tests which is impossible since if you miss 1 you're already down to a 90/A.

I'm the only person in the class with an A right now, and it's only a 90. I'm pretty sure about half the class is failing. I have friends that are in college calc that say it's ten times easier than her class was, and I believe them.

D=

Well, congratulations on having a 90% grade! That sounds like a huge feat

I think I would agree with your friend from College, too. Generally, college calculus is maybe a bit harder than general secondary school calculus, which is generally fair and not like what yours seems to be, I think

However, I can't say the same for first year calculus courses in universities, haha. Mine is a "theory" course, and its crazy, D+ -- but very interesting! If you like math, read "Calculus," by Michael Spivak. I guarantee it will enlighten your view and understanding of math, D=