Answer in Trigonometry for Sam #267493

If tan θ = – sqrt(3)/3 and cos θ > 0; Find csc θ.

let “theta” = k

Now, tan k = – (“sqrt3” / 3) = – (1/“sqrt3” )

cos k > 0

Now tan k is negative when k lies in second or fourth quadrant. And cos k is positive in first and fourth quadrant.

So we can infer that k lies in the fourth quadrant.

Now tan k = – (1/“sqrt3” ) => k = – 30“degree” => k = (360 – 30)“degree” = 330“degree”

So k = 330“degree”

Now cosec k = cosec 330“degree” = cosec (360 – 30)“degree” = – cosec 30“degree” = -2

therefore the answer is -2.