Question

determine the quadrant in which theta lies if sec theta <0 and tan theta >0

Answer 1

@johnweldon1993

Answer 2

Well we know that

\[\large sec(x) = \frac{1}{cos(x)}\]

And we want that to be less than 0...so when is

\[\large \frac{1}{cos(x)} < 0\]?

Answer 3

ok

Answer 4

so so far we have quadrants 2 and 3

Answer 5

Now:

\[\large tan(x) = \frac{sin(x)}{cos(x)}\]

When is that greater than 0? well it would mean either BOTH cos and sin are negative..or they are BOTH positive...

That happens