The correct question is <span>Given cos theta=4/9 and csc theta < 0 find sin theta and tan theta </span> we know that csc theta=1/sin theta if csc theta < 0 then sin theta < 0
we have that <span>cos theta=4/9
we know that sin</span>² theta+cos² theta=1 so sin² theta=1-cos² theta-----> 1-(4/9)²----> 1-(16/81)----> 65/81 sin theta=-√(65/81)---->-√65/9
the answer Part a) is sin theta=-√65/9
Part b) find tan theta
tan theta=sin theta/cos theta tan theta=(-√65/9)/(4/9)-----> tan theta=-√65/4
