Question 1094865
 could you please help me with this question

If x is in Quadrant IV with cos(x) = 3/5 and y is in Quadrant III with sin(y) = −2/√5, find cos(x+y)

I keep on getting -2√5 but that answer is not correct
<pre>cos (x + y) = cos x cos y - sin x sin y</pre>
<b><u>Q IV</b></u><pre>
{{{matrix(1,3, cos (x), "=", 3/5)}}}
{{{matrix(1,3, sin (x), "=", - 4/5)}}}</pre>
<b><u>Q III</b></u><pre>
{{{matrix(1,5, sin (y), "=", (- 2)/sqrt(5), or, - 2sqrt(5)/5)}}} ----- Easier to work with a RATIONALIZED denominator
{{{matrix(1,5, cos (y), "=", - 1/sqrt(5), or, - sqrt(5)/5)}}} ------ Easier to work with a RATIONALIZED denominator</pre>
<pre>cos (x + y) = cos x cos y - sin x sin y
{{{matrix(1,3, cos (x + y), "=", (3/5) * (- sqrt(5)/5) - (- 4/5) * (- 2sqrt(5)/5))}}}
{{{highlight_green(matrix(1,3, (- 3sqrt(5)/25) - 8sqrt(5)/25, "=====>", -
 11sqrt(5)/25))}}}