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Finding roots of this trig eqn

  • #1
utkarshakash
Gold Member
855
13

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?
 

Answers and Replies

  • #2
haruspex
Science Advisor
Homework Helper
Insights Author
Gold Member
32,401
4,909

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?
 
  • #3
utkarshakash
Gold Member
855
13
What are the lowest possible values of the two terms on the left? How can they add to -3?
That was helpful. Thanks!
 

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