Question

the following is a point not on a unit circle. θ → (-5,4) use it to find:

1. cos θ = -5
2. csc θ = 1/4

am i correct?

also, sec θ is negative, tan θ is positive. in what quadrant is < θ?

Answer 1

of course not. You know that cosθ is never greater than 1 or less than -1.

Similarly, cscθ is never less than 1.

Given a point (x,y),
r^2 = x^2+y^2

cosθ = x/r
cscθ = r/y

Also, given that cosθ<0 and cscθ>0. tanθ cannot be positive.

Answer 2

1. cos θ = .284
2. csc θ = 1.043
is this correct?
and would it be quadrant 3?

Answer 3

For the point (-5,4)
x = -5
y = 4
r = √41

cosθ = x/r = -5/√41 = -.781
cscθ = r/y = √41/4 = 1.601

Clearly the point is in QII !

How did you come up with your values?

Answer 4

i wrote quadrant 2 but my teacher said it was wrong