Question

Find cotangent theta given that cosecant theta equals -3.5891420 and theta is in the third quadrant.

I was using the trig identity 1+cot^2theta=csc^2theta

I wanted to isolate cotangent so I plugged in 1/sin (-3.5891420) and then squared my answer. I then subtracted one from both sides and sqaured both sides. I am getting 15.9427 when the answer is 3.44701905

please let me know where I am going wrong.

Answer 1

since 1+cot^2theta=csc^2theta
cot^2 Ø = csc^2 - 1
= (-3.589142)^2 - 1
= 11.8819403
cotØ = ± √11.8819403
= ± 3.447...
but since Ø in in III, cotØ must be positive, so
cotØ = 3.447..

Why were you doing
1/sin(-3.58914...) ????

-3.58... is NOT an angle, the csc(of some angle ) = -3.58...