Find tan((u)/(2)) if tan u = -13.348 and u is in...

Transcript

00:01 We need to find a value of tan of u over two if cost u is given to us and u is in quadrant two okay so i think a half angle identity would come in handy over here because we know that cost of u is nothing but one minus tan square u over two over one plus tan square u over two we have the value of cost you already but since we need to find the value of tan u over two for the moment i'm going to to substitute tan u or tan of u over two as y so that the calculation becomes a little easy and i'm going to i'm going to solve for y because y needs to be isolated now so cos u will be equal to 1 minus y square over 1 plus y square if we cross multiply then this will become 1 plus y square times cosine of u is 1 minus y square so uh if we distribute the left side left side that's going to be equal to cost u plus u plus y square cost u as equal to 1 minus y square and let's add y square both sides because we need to club all the y squares together so if we add y square both sides this will become y square plus y square cost u and if we subtract cost you both sides this will be one minus cost u so the value of y square if taken as a common factor is y square times one plus cost u is one minus cost u so the value of y square comes out as one minus cost u over one plus cost u uh and y is nothing but tan square tan u over two so that becomes tan square u over two is one minus cost u over one plus cost u and remember that if we take square root now both sides so we'll end up with plus and minus sign so although we'll end up with plus and a sign but we are given some information in which we can rule out one of the sign how is that because we are given that u is in quadrant two so uh it's given that u is in quadrant two it means that it is more than pi over two and less than pi and if we divide both sides by two then this becomes pi over four this becomes you actually all three sides by two uh this becomes u over two and this becomes pi over two and clearly more than pi over four and less than pi over 2 will imply that this is in quadrant 2 u over 2 and if you over i'm sorry this is in quadrant 1 so since u over 2 is in quadrant 1 so definitely tan has to be positive because in quadrant 1 all the trigonometric functions are positive so tan of u over 2 is going to be equal to root of 1 minus cos u over 1 plus cost u and what is cost you uh cost u is given to us as negative 0 .618 negative 0 .618 negative 0 .618 over 1 plus again negative 0 .618 so uh two negatives have become positive so that's 1 plus 0 .618 over 1 minus 0 .618.

03:25 So that's going to be, that's going to be one point.

03:33 Let me just grab my calculator 1 .618 over 1 minus 0 .618.

03:44 So the square root of this value comes out as we have to round to four decimal places...