Question

-2sin^2(x)-1cos(x)=-1
Looking for the smallest non-negative solution and the next smallest non-negative solution
Smallest non-negative solution: 0, ?
Next smallest non-negative solution: 360, ?

Answer 1

\[2\sin ^{2}x+\cos x=1\]
\[2-2\cos ^{2}x+cosx=1\]
\[2\cos ^{2}x-cosx-1=0\]
What do you get on solving this?

Answer 2

So far I have:

-2sin^2(x)-cos(x)=-1
-2(1-cos^2(x))-cos(x)=-1
-2+2cos^2(x)-cos(x)=-1
2cos^2(x)-cos(x)-1=0
(cosx-1)(2cosx+1)=0
cosx=1 or cosx=-1/2
x=0,360,720,... or x=120, 240, ...
therefore, Smallest non-negative solution=0
and the next smallest non-negative solution =120

But I've inputed:

The smallest non-negative solution is: 0 (0.5/1)
The next smallest non-negative solution is: 360 (0.5/1)

The Number in the brackets are the points that I've received so it looks like I'm missing something numbers. I've tried putting 120 for the second number in the "next smallest non-negative solution" spot and it said that was wrong.

Answer 3

Maybe you should have excluded 0, because it can be both positive and negative. -0 is the same as 0.
The smallest non-negative solution is: 120 The next smallest non-negative solution is: 360

Answer 4

0 and all positives are non-negative.

Answer 5

0
2.094395....
4.188790....

Answer 6

These are the first 3 non negative....