Generel Solution of sinx+cos^2 x= 1

[Superposed_Cat]

Hey all, I had this problem the other day, I had to find the generel solution of cos^2x+sinx=1 what I did was:
Sinx=1-cos^2x
Sinx=sin^2x
-sin^2x+sinx=0
(-Sinx-1)(sinx+0)=0
Sinx=0 or 1 so x=90+360n or x=0+360n but the textbook says "n/a and 90+360n" without showing any working out. Any help apreciated, apologies if this isn't the right thread but this isn't homework and there didn't seem to be a section for this under the homework anyway.

 

[lurflurf]

Textbook seems wrong what does n/a even mean? What is a?

x=90+360n or x=0+360n
are solutions but you missed some, can you think of the ones you mised?

 

[Superposed_Cat]

n/a they use for undefined or impossible like 2^x=0 would be n/a and tan90 would be n/a. Off the top of my head no I can't think of any other ones.

 

[EvilMarisa]

maybe the textbook's answer is wrong. so far i get sin x = 1 which the other one is rejected. so x = 90. sometimes you shouldn't trust textbooks. they may have some typo error or something

 

[pwsnafu]

Yeah, the textbook looks wrong.
$\cos^2(0) + \sin(0) = 1^2+0=1$
So the textbook shouldn't be discarding it.

 

[Superposed_Cat]

maybe the textbook's answer is wrong. so far i get sin x = 1 which the other one is rejected. so x = 90. sometimes you shouldn't trust textbooks. they may have some typo error or something

why did you reject the other one?

 

[Vanadium 50]

You might want to plot it so you will know how many answers you are looking for.

 

[Nugatory]

This question belongs in the appropriate homework section. Usually, we would delete it and ask that the original poster start a new thread in the right section and using the homework template. In this case the discussion has brought out most of the points that the template would cover, so I'm moving it instead.

 

[mfb]

n/a they use for undefined or impossible like 2^x=0 would be n/a and tan90 would be n/a. Off the top of my head no I can't think of any other ones.

You missed solutions for sin(x)=0. You found some, but not all.