>> Let's use identities to solve this problem. It says if sign theta is equal to six tenths find cosine theta and tangent theta. Now let's understand that we don't have to use identities to solve this problem. We could just take the tactic well if sign theta is six-tenths than I can make a little triangle here, a little right triangle and if this is theta, the sign of theta is opposite over hypotenuse and I just need to make a fraction that is equal to six tenths. It could be six tenths over 1 and I could make this six tenths or this 1 or I could say six tenths is six over ten, so I could make this side six and this side ten or I could say six over ten is the same as three-fifths, so I could make this side three and this side five. So there are a lot of ways to set up a situation using a triangle in order to go through and find the third sign you see and then find cosine theta and tangent theta. All right, all of that is fine, but let's use identities here to solve the problem. Now to use identities, here is what we do. We think well we have information about the sine and we want to find the cosine of theta. Now we need an identity therefore that involves sine and cosine and the convenient identity I am thinking about is the first Pythagorean identity that we looked at and it was that sine oops, it was that sine, squared theta, plus cosine squared theta is equal to 1 and then we just plug in the information we know. We know that sine theta is six tenths and we know that sine square theta means sine theta all squared so this becomes six tenths squared plus cosine squared theta equals 1. This becomes 36/100s. Then we subtract 36/100s on both sides and on the left, we will be left with cosine squared theta. On the right, we have 1 minus 36/100s turns out to be 64/100s and now if cosine square theta is equal to this value, cosine theta is equal to plus or minus the square root of that value. We want the positive one of those two, so it is the square root of 64/100s or .8. Now let's find tangent theta. Well one way to find tangent theta might be to look for an identity involving tangent and sine, but we have already calculate cosine theta, so we can involve an identity that has sine theta, cosine theta and tangent theta in it and that is pretty easy. That is the one that has tangent theta equals sine theta over cosine theta. Now when you use identities like this, I suggest that you write the identity down as I have here and not try to plug into the identity as you go along. So I would write the identity and then kind of plug into it, as thought it was a formula from the past. So tangent theta then is sine theta, we know is .6 and sine theta we calculated to be 8/10s so tangent theta then is 6/10s over 8/10, 6/8 or reducing 3/4.