Question 1178933

if tan(a) = -2, find the exact value of sin(a) and specify each possible quadrant
<pre>Correct answer: {{{highlight_green(matrix(1,4, Quadrants, 2, and, 4))}}}
{{{matrix(1,3, tan (a), "=", - 2)}}}
{{{matrix(1,9, tan (a), "=", O/A, "=", (- 2)/1, or, 2/- 1, "=", y/x)}}}
{{{matrix(1,9, r^2, "=", x^2 + y^2, "=", "(- 1|1)"^2 + "(2|- 2)"^2, "=", 1 + 4, "=", 5)}}}
{{{matrix(1,3, r, "=", sqrt(5))}}}
{{{highlight_green(matrix(1,7, sin (a), "=", O/H, "=", y/r, "=", "(- 2|2)"/sqrt(5)))}}}
{{{highlight_green(matrix(1,5, sin (a), "=", (- 2sqrt(5))/5, or, 2sqrt(5)/5))}}} 
With {{{highlight_green(matrix(1,3, sin (a), "=", (- 2sqrt(5))/5))}}}, and tan (a) = - 2, sin (a) is in QUADRANT IV. 
With {{{highlight_green(matrix(1,3, sin (a), "=", 2sqrt(5)/5))}}}, and tan (a) = - 2, sin (a) is in QUADRANT II.