sec theta = -3, tan theta > 0. Find the exact value of the remaining trigonometric functions of theta.

Dottie Parra

Dottie Parra

Answered question

2021-01-04


secθ=3,tanθ>0. Find the exact value of the remaining trigonometric functions of
θ.

Answer & Explanation

bahaistag

bahaistag

Skilled2021-01-05Added 100 answers

We have given the value of a trigonometric function sec(θ) and asked the values of other remaining trigonometric functions. So here we will use some standard identities and results in order to determine the values of other trigonometric functions.
sec2θtan2θ=1
cosθ=1secθ
sinθ=tanθsecθ
cosecθ=1sinθ
cotθ=1tanθ
Since, secθ=3<0andtanθ>0 then θ must be in third quadrant in which sinθ,cosθ,cosecθandsecθ will be negative and rest tanθandcotθ will be positive.
Now,
sec2θtan2θ=1
(3)2tan2θ=1
tan2θ=(3)21
tanθ=8
Also,
cosθ=1secθ=13=13
sinθ=tanθsecθ=83=223
cosecθ=1sinθ=1223=322
cotθ=1tanθ=18=122
Hence, values of other trigonometric functions sinθ,cosθ,tanθcosecθandcotθ will be 223,13,22,322and122 respectively.
Jeffrey Jordon

Jeffrey Jordon

Expert2021-12-14Added 2605 answers

Answer is given below (on video)

Jeffrey Jordon

Jeffrey Jordon

Expert2022-02-01Added 2605 answers

Answer is given below (on video)

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