Question

What is the trig identity for cos^2x=(half angle)???
help!

Answer 1

http://tutorial.math.lamar.edu/pdf/Trig_Cheat_Sheet_Reduced.pdf

Answer 2

\[\cos(2x)\] or
\[\cos^2(x)\]?

Answer 3

@satellite73 ???

Answer 4

which one is it?

Answer 5

oh, it's the latter

Answer 6

the only thing i know to do with \(\cos^2(x)\) is to rewrite is as \(1-\sin^2(x)\)

Answer 7

http://tutorial.math.lamar.edu/pdf/Trig_Cheat_Sheet_Reduced.pdf

Answer 8

O.O!

Answer 9

I saw the formula, but I don't know how you would derive that... and especially when you also have a double angle thrown in there... LOL

Answer 10

it has nothing to do with double angle
it comes from the basic
\[\sin^2(x)+\cos^2(x)=1\]

Answer 11

the half angle formula comes from that?!? relly?

Answer 12

how

Answer 13

i didn't mention the half angle formula

Answer 14

the half angle formula comes from taking the double angle formula for cosine and replacing \(2x\) by \(x\)

Answer 15

...

Answer 16

?

Answer 17

You mean the cos2x=cos^2 x - sin^2 x ?

Answer 18

\[\cos(2x)=\cos^2(x)-\sin^2(x)\] replace \(2x\) by \(x\) and \(x\) therefore by \(\frac{x}{2}\)

Answer 19

then are you supposed to square it?

Answer 20

Ok I plugged them in... Now what?

Answer 21

ok hold the phone i gave you the wrong formula to use

Answer 22

\[\cos(2x)=2\cos^2(x)-1\] use that one

Answer 23

oh, ok. Will the other one not work even though they're the same?

Answer 24

no the other has both sine and cosine
no help

Answer 25

oh, ok that makes sense LOL

Answer 26

you get
\[\cos(x)=2\cos^2(\frac{x}{2})-1\] and you solve this for \(\cos(\frac{x}{2})\)

Answer 27

ok done

Answer 28

ahhh and THIS is where you need \(\pm\)!!

Answer 29

Oh! hahaha good thing I asked that before hand

Answer 30

wait... where does the plus and minus fit in?

Answer 31

I got cos^2 (x/2)=[ cos(x)+1 ]/2

Answer 32

yeah right

Answer 33

oh... the next step

Answer 34

but you want to get rid of the square
yes next step

Answer 35

but be careful
even though there is a \(\pm\) in the formula, doesn't means you get two answers
you have to decide if it is plus or minus

Answer 36

by looking at the domain that they give you in the problem, right? What do you look at to determine that?

Answer 37

This is what I got:
cos(x/2)= (+-) ROOT[(cosx +1)/2]

Answer 38

what quadrant your angle is in

Answer 39

\[\cos(x)=\pm\sqrt{\frac{\cos(x)+1}{2}}\]

Answer 40

course it is on the cheat sheet as well

Answer 41

actually it is really good to know how to derive these because who can memorize all this drek
easy to know a few and then get the ones you need

Answer 42

yes, but why does that one have a double angle in it? even if you take the root, there's a double angle in it...

Answer 43

you lost me

Answer 44

yeah, it's what I do with my sin^2 +cos^2=1

Answer 45

ok wait a sec

Answer 46

cos^2 x=(1/2) (1+cos(2x))

Answer 47

thats wat it says on the sheet

Answer 48

fine
then take the square root and get exactly what you got before

Answer 49

oh, and replace \(x\) by \(\frac{x}{2}\)

Answer 50

oh! So THAT's what happened! LOL that was simple.

Answer 51

I was like, why is there a double angle in this formula..? hahaha

Answer 52

yeah simple enough

Answer 53

why trig so early in the semester?

Answer 54

Oh, and I need some geomeetry brushing up to do, I'll open a new question for it... I can memorize these geo. volume and are formulas all I want, but I won't understand thme and be able to use them...

Answer 55

have fun

Answer 56

Are you leaving?

Answer 57

:) thanks for your time~ I really appreciate it a lot!