Trig problem

  • #1

Homework Statement


Find cscθ given sec θ = -2 sin θ >0

Homework Equations


I do not know where to begin or what equations to use.

The Attempt at a Solution


I am assuming there is a typo in the question and that there should be a comma sec θ = -2, sin θ >0.

If so I got csc θ = 2√3 / 3
 

Answers and Replies

  • #2
SteamKing
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Homework Statement


Find cscθ given sec θ = -2 sin θ >0

Homework Equations


I do not know where to begin or what equations to use.

The Attempt at a Solution


I do not know where to begin or what equations to use.
Why not? How is the secant defined? The cosecant? Those would be good places to start.
 
  • #3
I am assuming there is a typo in the question and that there should be a comma sec θ = -2, sin θ >0.

If so I got csc θ = 2√3 / 3
 
  • #4
SteamKing
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I am assuming there is a typo in the question and that there should be a comma sec θ = -2, sin θ >0.

If so I got csc θ = 2√3 / 3
Looks good.
 
  • #5
Ray Vickson
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Homework Statement


Find cscθ given sec θ = -2 sin θ >0

Homework Equations


I do not know where to begin or what equations to use.

The Attempt at a Solution


I am assuming there is a typo in the question and that there should be a comma sec θ = -2, sin θ >0.

If so I got csc θ = 2√3 / 3
The question as written (no comma) also makes perfectly good sense; it says that ##0 < \sec \theta = - 2 \sin \theta##, and you need to use the definition of ##\sec## to get a solvable equation. You can get ##\sin \theta## and ##\cos \theta##, then compute ##\csc \theta##, which does NOT equal ##2 \sqrt{3}/3 = 2/\sqrt{3}##.
 
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  • #6
SammyS
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Homework Statement


Find cscθ given sec θ = -2 sin θ >0
As Ray points out, the problem as stated makes sense and can be solved. If you are currently studying trig equations in your course, then that's probably not a typo. On the other hand, if you are studying the basics of trigonometric functions early in your course, then it very well may be a typo, similar to what you have concluded.

The statement, ##\ \sec θ = -2 \sin θ >0 \,,\ ## is really two (or three) statements rolled into one.
  • ##\ \sec θ >0 \ ##
  • ##\ -2 \sin θ >0 \,,\ ## so that ##\ \sin θ <0 \ ##
  • ##\ \sec θ = -2 \sin θ ##
The first two tell you what quadrant θ is in.
 
  • #7
Dr Transport
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recast [itex] sec(\theta) [/itex] as [itex] 1/cos(\theta) [/itex] and the solution falls out in about 2 lines...
 

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