CREDIT) Score: 27.41/50 "27/50 answered Progress saved Done VoQuestion 43C1pt 01 299Without using a calculator; compute the sine and coslne 0f 315 by using the...

Evaluate the trigonometric function of the quadrant angle, if possible. $$\sec \frac{3 \pi}{2}$$

Here we have the given information and our goal is to find the sign of B minus you. And according to our difference formula, the sign of V minus you would be the sign of B times, a co sign of U minus the coastline of e times. A sign of you. We know a couple of those values and we're going to need to figure out the other ones. So using are given information and knowing that both angles Aaron Quadrant two. Let's draw a reference triangle for both. So for you, we know that the Sinus 5/13 So we can put five on the opposite and 13 on the high pot news. And if we use the Pythagorean theorem, we get 12 for the adjacent and then pervy also in quadrant two. We know the coastline is negative 3/5. So we could put three on the adjacent and five on the high pot news and use the Pythagorean theorem, and we get four for the opposite. Okay, so the sign of e from the bottom triangle would be 4/5. The coastline of you from the top triangle would be negative. 12 13th The coastline of the We were given negative 3/5 and the sign of you we were given 5/13. So let's simplify this. When we multiply the 1st 2 fractions together, we get negative 48 65th and then we have minus negative. So that's plus and then we multiply the last two fractions. Together we have 15 65th. And then when we had these fractions, we end up with negative 33 65th.

Our goal in this problem is to find the Cosi can't of u minus v. I'm actually going to start by finding the sign of U minus feet and then I'll take the reciprocal at the end. And according to our difference formula, the sign of U minus B is the sign of you times a coastline of e minus the coastline of you times a sign of E. Now we know the sign of you that was given, and we know the coastline of E that was given. And let's make a reference triangle for both of these so we can find the other numbers. So both you and beer in Quadrant two and the sign would be opposite over high pot news. And if we use the Pythagorean theorem, we get 12 for the other side. And then V also in quadrant two coastline is adjacent over high pot noose. And if we use the Pythagorean theorem, we get four for the opposite side. Okay, so now back to what we're figuring out sign of you. That was 5/13 coastline of V. That was negative. 3/5 minus co sign of you. We confined that negative 12 13th remember? Coastline is negative in quadrant two and sign of E. We confined that 4/5. Okay, so when we multiply the 1st 2 fractions, we get negative. 15 65th. Then we have minus negative. So plus and we multiplied the last two fractions, and we have 48 65th. So when we had those together, we get 33 65th. And that is the sign of U minus B. So the co sign Cosi can't of u minus b would be the reciprocal of that 65 33rd.

Here we have our given information, and our goal is to find the co sign of U minus B. And according to the difference formula, the coastline of U minus V is going to be coastline you times co sign be plus sign you time sign V. So we're going to need to find those missing pieces. So let's use our pieces of given information and draw reference triangles. We know U and V are both quadrant two angles, So I'm going to draw a reference triangle for angle you in Quadrant two. And we know the sign is 5/13 so the sign would be opposite over high pot news. And if you use the Pythagorean theorem, you'll get 12 on the other side and then privy. Same idea. And we know the co sign is negative. 3/5. So adjacent overhype odd news. And if you use the Pythagorean theorem, you'll get four for the other side. So now we have everything we need to find each of these four values. Coast I knew is going to be negative. 12 13th Coastline V was given negative 3/5 Sign You was given by 13th and signed B 4/5. Okay, so let's simplify this. Eso We have 36 65th plus 20 65th. Add those together and we have 56 65th.

To find the sea can't of three pi over two. I'm going to use the unit circle. So here's the center. The vertex of the angle is at the origin 00 and the initial ray of the angle is on the positive X axis. And then we go counterclockwise three pi over two radiance and that takes us to the negative y axis. And a point on the terminal side on the unit circle would be the 0.0.0 negative one. Now the X coordinate of the point is the coastline value on the Y. Coordinate of the point is assigned value and see Can't is the reciprocal of co sign. The reciprocal of zero is undefined, so the C can't of three pi over two is undefined.