Question

find all values of x in the interval (0,2pi)that satisfy cos^(2)x + sinx = 1

Answer 1

I would start by using the trig identity cos^(2)x = 1 - sin^(2)x.

Answer 2

I added the interval of (0,2pi) to my question.

Answer 3

You can try solving it using @lncognlto's substitution, bring the terms to one side to get a form " = 0 " then you can just think of "sin x" as just be "x", and then you can factor the "polynomial" and then resubstitute x for sin x (if you can do the substitution mentally, you don't actually have to write down the substitution as is)

Answer 4

Thanks to both of you.

Answer 5

So my formula would look like this? cos^(2) + sinx - 1 = 0?

Answer 6

cos^2(x) + sinx = 1
sin(x) = 1 - cos^2(x)
sin(x) = sin^2(x)
sin^2(x) - sin(x) = 0
sin(x) * ( sin(x) - 1 ) = 0
sin(x) = 0 or sin(x) = 1
find all x in the given interval where the above is true.

Answer 7

thanks to all of you I get it now...too much rust on this old brain of mine.

Answer 8

yw.

Answer 9

Sorry tried to give all of you best response but I couldn't