Question

If cos theta is less than 0 and cot theta is greater than 0, then the terminal point determined by theta is in:

A. Quadrant 2
B. Quadrant 3
C. Quadrant 1
D. Quadrant 4

Answer 1

if cosine is < 0
and cotangent > 0
but
\(cot(\theta)=\cfrac{cos(\theta)}{sin(\theta)}\)
so if the numerator there is negative, cosine < 0
to get a positive off the fraction, you'd also need a negative sine, that is sine < 0
now on which Quadrant are sine and cosine negative?

Answer 2

The 3rd quadrant

Answer 3

so, there's the terminal point :)

Answer 4

Oh I get it. So what if it said cotangent theta > 0. Then what would it be?

Answer 5

well, in this case cotangent is >0, so it'd be the 3rd one :)

Answer 6

now if the cotangent were negative, then what you have would be \(cot(\theta)=\cfrac{-cos(\theta)}{+sin(\theta)}\)

Answer 7

because the fraction, since the cosine is negative, < 0, will need a positive in the denominator to become negative
then at Quadrant II cosine is negative and sine is positive

Answer 8

Thanks soooo much!

Answer 9

yw