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March 27, 2017

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Given \tan \theta = -\frac{4}{3}, where \frac{\pi}{2} < \theta < \pi, what is the value of \frac{1}{\sin \theta + \cos \theta}?

  • Trigonometry - ,

    I will guess that you meant:

    tanØ = 4/3, π/2 < Ø < π , or Ø is in quadrant II
    construct the right-angled triangle, and you should recognize the 3-4-5 triangle.

    guessing that you want:
    1/sinØ + cosØ

    in II, the sine is + , but the cosine is -
    sinØ = 4/5 and cosØ = -3/5

    1/sinØ + cosØ
    = 1/(4/5) + (-3/5)
    = 5/4 - 3/5
    = 13/20

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