Find sin(u/2) if tan(u)=-7.721 and u is in quadrant 4

.6601

Step-by-step explanation:

to find u, which we assume is an angle of course, we can take arctan of both sides.  so arctan(-7.721) = -1.4420.  this angle is in quadrant 4, but it is not in the range.  In this instance you just go around the circle again, or add 2pi, which gets us 4.8412.  You can check and you get the same answer if you take the tangent of either.

So now we have a number in the appropriate range  in the appropriate quadrant.  That means we have the correct angle.  The question asks what is sine of that angle cut in half.  so sin(4.8412/2), which gets you your answer.  let em know if something didn't make sense.  

8

step-by-step explanation: