Question 1034092

Find tan t given that sin t=3/5 and cot t < 0
<pre>sin is positive (> 0), and cot is negative (< 0), so t is in the 2nd quadrant. Also since cot is < 0, tan will also be < 0
{{{sin (t) = O/H = 3/5 = y/r}}}
Since y = 3 and r = 5, this is a 3-4-5 Pythagorean triple. Hence, x = - 4 (x is < 0 in the 2nd quadrant)
{{{highlight_green(matrix(1,5, tan (t), "=", O/A = y/x = 3/(- 4), or, - 3/4))}}}