Question 1061978

If sin theta = -5/13 and theta terminates in 3rd quadrant find cos theta and tan theta.
<pre>{{{sin (theta) = (- 5)/13 = O/H = y/r}}}
With y = - 5, and r = 13, we have a 5-12-13 Pythag-triple triangle
Therefore, x MUST = - 12 (x is NEGATIVE in 3rd quadrant)
{{{highlight_green(matrix(1,9, cos (theta), "=", A/H, "=", x/r, "=", (- 12)/13, or, -12/13))}}}
{{{highlight_green(matrix(1,9, tan (theta), "=", O/A, "=", y/x, "=", (- 5)/(- 12), or, 5/12))}}}