Question 1161413

If cos x= -15/17 with x in quadrant III, find the exact value of sin 2x and the quadrant of 2x
<pre>You may be able to recognize this TRIG function as an 8-15-17 PYTHAG. TRIPLE.
We have: {{{matrix(1,7, cos (x), "=", A/H, "=", (- 15)/17, "=", x/r)}}}
As x is in QIII, we get: y = O = - 8, and so, {{{matrix(1,7, sin (x), "=", O/H, "=", y/r, "=", (- 8)/17)}}}
{{{matrix(1,3, sin (2x), "=", 2 sin (x) cos (x))}}}
{{{highlight_green(matrix(1,7, sin (2x), "=", 2 * ((- 8)/17) * ((- 15)/17), "=", 2(- 8)(- 15)/17^2, "=", highlight(240/289)))}}}
Can you now tell which quadrant 2x lies in?