# Should I know trignometric identitys?

1. Jun 11, 2009

### vorcil

my question is, should a first year after finishing first semester
(going through exams at the moment)
know things about trignometric identitys?, i haven't come across them YET in any of my papers nor highschool.
I'm a first year physics and engineering major,

and i had come across a question that involved a trignometric identity in a physics derivation question,
and i didn't know how to solve it
so i got some help and a guy told me to use trignometric identitys

i've never really heard of them (or most probably only know the basic ones without knowing it)

it was something like (velocity^2)*2sin(theta)*cos(theta) or something like that = sin(2theta), i had to research online and it took me ages to find this

cheers

2. Jun 11, 2009

### vorcil

I know the basic ones like costheta*tantheta=sintheta
but i've only learnt them by memorization, i have no idea where they come from and whatnot

3. Jun 11, 2009

### Cyosis

Shouldn't take you ages to find a site with those identities, http://en.wikipedia.org/wiki/Trigonometric_identitiesp [Broken] has tonnes of them. That said you should really know the basic ones and those you don't know by heart you should be able to derive. The most important of all is probably $\cos^2x+\sin^2x=1$, never forget it!

Trigonometry is used a lot in physics so it is really important to be proficient at working with trig identities. If you know complex numbers many of the identities are very easy to derive.

Last edited by a moderator: May 4, 2017
4. Jun 11, 2009

### HallsofIvy

Hopefully, you should know that $sin^2 x+ cos^2 x= 1$! That's probably the most important identity. I don't know what courses you have taken so I can't say what you "should" know.

Past, $sin^2 x+ cos^ x= 1$, it is certainly useful to know the "sum" formulas, sin(x+ y)= sin(x)cos(y)+ cos(x)sin(y) and cos(x+y= cos(x)cos(y)- sin(x)sin(y) as well as the double angles formulas, sin(2x)= 2sin(x)cos(x) and cos(2x)= cos2(x)- sin2(x) that follow from them.

5. Jun 11, 2009

### Office_Shredder

Staff Emeritus
I didn't bother really learning them until I reached university and that was a mistake. I stumbled a lot on trickier integrals and other things because I didn't recognize the right trig identity to use

If you're only going to see one integral your whole life that requires trig identities then you're fine, but don't be surprised if you reach a class where you need to do two a day and the whole thing comes crumbling down (well, for the two hours it takes to review all of them again :) )

6. Jun 11, 2009

### tiny-tim

Hi vorcil!
Yes, definitely learn all the simplest ones …

see the PF Library on trignometric identities (and spell it right! )

7. Jun 12, 2009

### qntty

The sum and difference identities (you only need to know the sum and can derive difference) are the only ones which are difficult to derive. The rest (sum to product, half angle, double angle) can be derived from that.

8. Jun 14, 2009

### rochfor1

Seriously? tan = sin/cos.

9. Jun 14, 2009

### tiny-tim

Very elementary trigonometric identities …

sin = opp/hyp,

and so tan = sin/cos

10. Jun 14, 2009

### Redbelly98

Staff Emeritus
I think these 2 posts pretty well summarize what should be remembered (I did some editing for organization/clarification):

11. Jun 15, 2009

### Irrational

we always remembered it as sohcahtoa. nice and easy.

12. Jun 15, 2009

### Irrational

knowing trig identities makes problems like https://www.physicsforums.com/showthread.php?t=320029" very easy. otherwise it's very easy to get bogged down.

Last edited by a moderator: Apr 24, 2017
13. Jun 15, 2009

### Cantab Morgan

As a couple of others have mentioned, I also urge memorizing the sum formulas sin(a+b) and so forth. I find myself using these all the time.

14. Jun 15, 2009

### Pengwuino

Expressing the trigonometric identities as
$$\begin{array}{l} e^{ix} = \cos (x) + i\sin (x) \\ \sin (x) = \frac{{e^{ix} - e^{ - ix} }}{{2i}} \\ \cos (x) = \frac{{e^{ix} + e^{ - ix} }}{2} \\ \tan (x) = \frac{{e^{ix} - e^{ - ix} }}{{i(e^{ix} + e^{ - ix} )}} \\ \end{array}$$

makes a lot of identities almost trivial to prove. I proved sin(x+y)=sin(x)cos(y)+sin(y)cos(x) in 4 lines just now using it. This is quite helpful since my memory is about as short as the proof :rofl: .

Trigonometric identities become insanely important as you continue your physics courses. Up until a few years ago, I swear i basically knew $$\sin ^2 x + \cos ^2 x = 1$$ and that was it :rofl: . Whenever a trig function popped up in a question, i basically was stranded. Now I still have only that identity memorized practically but have the tools to immediately pop out any trig identity I need using the complex formulations of the trigonometric identities. It makes homework easier. You definitely need as few roadblocks while doing your homework as possible!

15. Jun 16, 2009

### qntty

you can use the rotation matrix too

$$\begin{bmatrix} \cos x & \sin x \\ -\sin x & \cos x \end{bmatrix} \begin{bmatrix} \cos y & \sin y \\ -\sin y & \cos y \end{bmatrix} = \begin{bmatrix} \cos (x+y) & \sin (x+y) \\ -\sin (x+y) & \cos (x+y) \end{bmatrix} = \begin{bmatrix} \cos x \cos y -\sin x \sin y & \cos x \sin y + \sin x \cos y \\ -\cos x \sin y - \sin x \cos y & \cos x \cos y -\sin x \sin y \end{bmatrix}$$

16. Jun 16, 2009

### Pengwuino

I like the exponential notation because you can prove things like the decomposition of $$\cos ^5 (x)$$ into linear terms fairly easy whereas in all honesty I don't even think i'd know how to do it otherwise haha.