Compund Angles (1 Viewer)

[hbk_873]

Hey everyone, have first 3u test on monday.
In the further trig topic it has Compund Angles?
Does anyone know what compound angles are? i havent come across the term compound angles before
Is it just the identities like Sin (a+b) = ?

we also have double angles, thats just sin2a right?

sorry for asking a stupid question, just wanna make sure im not missing out on studying something

 

[Xayma]

I havent heard the term compound angles so I cant help you there however, double angles is the things like sin2a=2sin(a)cos(a)

 

[flyin']

I'm not sure what you're asking but:

Compound angles should be:
sin(A+B) = sinAcosB + sinBcosA
cos (A+B) = cosAcosB - sinAsinB

And from the above you get: (by substituting B = A)
sin2A = 2sinAcosA
cos2a = (cosA)^2 - (sinA)^2
= 2(cosA)^2 - 1
= 1 - 2(sinA)^2

 

[...]

haha, shit..flyin' still remembers his stuff

i think compound angle is the tan formula one..

 

[Redp3n]

Scipio Africanus Mother Fuckus

 

[flyin']

But I've used these once or twice this semester, so I still remember a little. And I am enrolled in a Mathematics degree.

 

[freaking_out]

yeah, compound angles is sin (a+b) and sin2a, as well as for tan and cos ofcourse....also ask ya teacher for textbook references, if ur not sure as to what exactly is in the test.

a for flyin': he gets high on maths textbooks (which u have to do if u wanna b an actuary) thats why he has no trouble remembering these things.

 

[Rahul]

oh god! i hated these.

spent good time trying to remembering them by writting them out over and over again.

 

[mercury]

LOL, trig is not about rote learning, the best way to know your formulae is through:
(1) knowing how the formulae came about
(2) doing exercises

Trig Identities

Things like (cosa)^2 + (sina)^2 = 1, are easily derived by considering triangles (going back to fundamental definitions of trig), then deviding both sides by (cosa)^2 or (sina)^2 will give you the two other identities

Compound Angles

sin(a+b) = sinacosb + sinbcosa
cos(a+b) = cosacosb - sinasinb
tan(a+b) = tana+tanb/1-tanatanb
etc. -> check fitzpatric/excel/cambridge
These are also derived from fundamentals of trig, ie. drawing two triangles and playing around with trig rules (sin: opposite side/hypotenuse, etc.)

Double Angles

sin2A = 2sinAcosA
cos2A= 2(cosA)^2 - 1 , etc.
tan2A = 2tanA/1-(tanA)^2
you can derive this by drawing a triangle with angle A and its reflection. The other way is of course from
sin(A+B). Similar reasoning for cos2A and tan2A

Half Angles

These are manipulation of the double angle formulae,
sinA = 2sin(A/2)cos(A/2)
cosA = 2(cos(A/2))^2 - 1
tanA = 2tan(A/2)/1-(tan(A/2))^2
etc. The application of these are mostly in the so-called t-results, which can be very useful when it comes to integration:

tan(x/2) = t

then through algebraic manipulation you get:

tanx = 2t/1-t^2
sinx = 2t/1+t^2
cosx = (1-t^2)/(1+t^2)

So these are just a brief note on standard trig formulae

 

[iambored]

never heard of that term... compound angles....