Question 1199614
<pre>
if tan 0= 2/3 and angle 0 is a principal angle that lies in a quadrant 3 such that 0° ≤ θ ≤ 360°, determine cos 0 and sin 0

As θ is in the 3rd quadrant, {{{matrix(1,9, tan (theta), "=", 2/3, "=", (- 2)/(- 3), "=", O/A, "=", y/x)}}}

                {{{matrix(1,11, Hypotenuse^2, or, r^2, "=", x^2 + y^2, "=", (- 3)^2 + (- 2)^2, "=", 9 + 4, "=", 13)}}}
                                  {{{matrix(1,3, r, "=", sqrt(13))}}}

               We then get: {{{highlight_green(matrix(2,9, highlight(cos (theta)), "=", A/H, "=", x/r, "=", (- 3)/sqrt(13), "=", highlight((- 3sqrt(13))/13), highlight(sin (theta)), "=", O/H, "=", y/r, "=", (- 2)/sqrt(13), "=", highlight((- 2sqrt(13))/13)))}}}</pre>