Cotangents....

Question

The cotangent of Θ is -1 and the cosine of Θ is sq. root of 2/2. What is the cosecant of Θ?

Answer 1

I must assume that you mean to find θ for which cotθ=-1 and cosθ=√2/2

The angle nearest the origin which satisfies these requirements is θ=-π/4

The csc0 is undefined. As the angle approaches 0 from the left the cosecant goes to -∞

as the angle approaches 0 from the right the cosecant goes to +∞.