Question 1198723

Given cot theta =-2 and csc theta < 0, find sin theta and sec theta
<pre>I'd advise you not to look at/Ignore that woman's response. 

As cot is negative, theta is either in quadrant 2 or 4. Since csc is also negative (< 0),
theta is either in the 3rd or 4th quadrant. Thus, theta is definitely in the 4th quadrant.

 {{{matrix(1,9, cot (theta), "=", - 2, "=", cos (theta)/sin (theta), "=", 2/(- 1), "=", x/y)}}}

     {{{matrix(4,3, r^2, "=", x^2 + y^2, r^2, "=", 2^2 + (- 1)^2, r, "=", sqrt(2^2 + (- 1)^2), r, "=", sqrt(5))}}}

{{{highlight_green(matrix(1,11, highlight(sin (theta)), "=", O/H, "=", y/r, "=", (- 1)/sqrt(5), "=", (- 1)sqrt(5)/(sqrt(5))^2, "=", highlight(- sqrt(5)/5))))}}}

{{{highlight_green(matrix(1,7, highlight(sec (theta)), "=", H/A, "=", r/x, "=", highlight(sqrt(5)/2))))}}}</pre>