melissavillanueva77 melissavillanueva77
  • 13-07-2021
  • Mathematics
contestada

Help! Given that tanθ=-1, what is the value of secθ, for 3π/2<θ<2π?

Help Given that tanθ1 what is the value of secθ for 3π2ltθlt2π class=

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jimthompson5910 jimthompson5910
  • 13-07-2021

Answer:  Choice B)  [tex]\sqrt{2}[/tex]

Work Shown:

[tex]\sec^2(\theta) = \tan^2(\theta) + 1\\\\\sec^2(\theta) = (\tan(\theta))^2 + 1\\\\\sec^2(\theta) = (-1)^2 + 1\\\\\sec^2(\theta) = 2\\\\\sec(\theta) = \sqrt{2}\\\\[/tex]

Note: secant is positive in quadrant Q4, when theta is between 3pi/2 radians and 2pi radians (270 degrees and 360 degrees). So that's why we don't consider the minus form of the plus minus.

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