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given that csc(theta) =-3 and cos(theta)>0, find the remaining 5 trigonometric functions of theta.

i have my triangle graphed in the fourth quadrant but I'm getting confused because of the negatives...

  • math -

    cscØ = -3 , so sinØ = -1/3

    the sine is negative in III and IV
    cosine is positive in I and IV
    so you are correct to say that Ø is in IV

    make yourself familiar with the CAST rule, here is an explanation for it

    So your triangle in IV should be a 1-√8 -3 triangle

    sinØ = -1/3 , cscØ = -3 (that was the given)
    cos = √8/3 , secØ = 3/√8
    tanØ = -1/√8 , cotØ = -√8

    (Your textbook answer might have written the √8 as 2√2 )

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