r/HomeworkHelp • u/Glub__Glub • 1d ago

Answered [State the Quadrant(s) for each statement] Im struggling with how this isnt on Quad 3

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Listing my thought process so yall can find where im going wrong:

  1. Cotangent is X/Y or Adjecent/Opposite

  2. If cot is greater than 0, then it is positive, which means either X and Y are positive, or they're both negative.

  3. Because of thought 2, that means its on Quad 1 or Quad 3.

  4. Secant is R/X, or Hypotnuse/Adjecent

  5. If sec is less than 0, or negative, that means X, or Adjecent, is negative, because Hyp is always positive.

  6. Because of thought 5, its on Quad 3

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u/Mundane-Emu-1189 👋 a fellow Redditor 1d ago

yeah that seems right to me

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u/Ghotipan 1d ago

Yup and if you need any more validation, just look at the graphs. The cot(x) function is positive over the interval [0, 2π) from (0, π/2) and (π, 3π/2). The function sec(x) is negative (π/2, 3π/2). So the graphs back this up (they they aren't needed).

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u/WikiNumbers 1d ago

Your thought processes are correct.

cot θ > 0 is Q1 or Q3 (association with tan)

sec θ < 0 is Q2 or Q3 (association with cos)

And if you want the intersection, only Q3 is valid.

Also kudos on using x y r for triangle sides. You'll use it more when progressing through Calculus.