Question

Let θ be an angle in quadrant III such csc(θ)=-(13)/(5)

Find the exact values of tan θ and cosθ ?

Answer 1

Draw a picture. If you're using trig functions it's a right triangle, and the only right triangle that works with 5 and 13 is [5, 12, 13] (keep in mind what csc is, it tells us that 13 is the hyp). Knowing this, I'm sure you can figure out everything else after drawing a picture.

Answer 2

it's complicated!

Answer 3

cscθ=-(13)/(5)
cscθ = 1/sinθ => sinθ = 1/cscθ = 1/(-13/5) = -5/13

So can you find tan θ and cos θ yourself?
remeber for quad. III, tanθ is positive and cosθ is negative!