Question

write the fallowing expression in terms of the first power of sine only.
sinz+cosz

Answer 1

Ah, the key here is getting cos in tems of sin.

Answer 2

i got this far
sinz+\[\sqrt{1-\sin ^{2}(2)}\]

Answer 3

then i got to \[\sqrt{2\sin(x+\frac{ \pi }{ 4 }}\]

Answer 4

That is one way to start. You used the half angle for the second step?

Answer 5

i think so. honestly i cant remember that was from school earlier..

Answer 6

The cofunction identities mught get you where you want faster. Know those?

Answer 7

noo?

Answer 8

Ah. Kk. Yah, if you are not yet allowed to use cofunction, then you are stuck with reucing that.

Answer 9

what is cofunction?

Answer 10

http://milkoskymath.blogspot.com/2011/02/cofunction-identity-proof_11.html

Answer 11

There is a similar one that applies more here: \[\cos z = \sin(\frac{\pi}{2}-z)\]

Answer 12

Which is like one step and there. Or you could use the proof in that video as a foundation to do this and show your work.

Answer 13

oksy i see that, how do i use that for my problem?

Answer 14

\[\sin z + \cos z = \sin z + \sin(\frac{\pi}{2}-z)\]

Answer 15

There are no powers in that, so i is in terms of sine to the first power.

Answer 16

what do you mean? do i simpilfy that answer? would it be cosz=sin\[\frac{ \pi }{ 2 }-z\]

Answer 17

No, that is simplified. It says terms. There are two terms and they single power terms of sine. There might be mroe that could be done with it, but that is an answer. The thing is, if you need to show work on it, the professor won't take it unles you can write the proof of the cofunction. In that video with the girl, she does that one starting at about 3 min in.

http://youtu.be/wVSgwRV2_o8?t=2m54s

Answer 18

That is why I said it is really easy if you are allowed to use cofunction. One step, done. But if not yet allowed to use cofunction, it is writing out the proof of cofunction, applying it, done.

Answer 19

she proves cos in the video is that what my problem is? i thought it was sine bc it says first power of sine?

Answer 20

She does one then does the other. You want to replace cos with something using sin, so that is the second part.

Answer 21

so for my work in my problem i would do what she does in the video?

Answer 22

Yes, that will give you a valid solution that is based on more basic identities. As long as you can prove each identity, or have done the previous ones in class, it is allowed. Usually you have done sum and differencce by the time you get half angle and power reduction, so you should be fine.

Answer 23

okay good deal.

Answer 24

Heck of a lot easier than dealing with getting stuff out of the root.

Answer 25

yeah foreal.