Finding roots of this trig eqn

[utkarshakash]

Homework Statement

If [sinx]+[√2 cosx]=-3, x belongs to [0,2∏] (where [.] denotes the greatest integer function) then x belongs to
1)[5∏/4,2∏]
2)(5∏/4,2∏)
3)(∏,5∏/4)
4)[∏,5∏/4]

The Attempt at a Solution

If I put x=5∏/4, LHS=-2 which does not satisfy. 2∏ and ∏ also does not satisfy.So the answer must be either 2) or 3). Is there any better way other than putting the values one by one and checking?

 

[haruspex]

Homework Statement

If [sinx]+[√2 cosx]=-3, x belongs to [0,2∏] (where [.] denotes the greatest integer function) then x belongs to
1)[5∏/4,2∏]
2)(5∏/4,2∏)
3)(∏,5∏/4)
4)[∏,5∏/4]

The Attempt at a Solution

If I put x=5∏/4, LHS=-2 which does not satisfy. 2∏ and ∏ also does not satisfy.So the answer must be either 2) or 3). Is there any better way other than putting the values one by one and checking?

What are the lowest possible values of the two terms on the left? How can they add to -3?

 

[utkarshakash]

What are the lowest possible values of the two terms on the left? How can they add to -3?

That was helpful. Thanks!