Question
4. Write the vectors below in the form of (r,0) (the polar coordinates). (4 Marks)[~V3,1][V3,-1]
4. Write the vectors below in the form of (r,0) (the polar coordinates). (4 Marks) [~V3,1] [V3,-1]
Answers
Express the following polar coordinates in Cartesian coordinates. $$\left(-4, \frac{3 \pi}{4}\right)$$
So we have a point in polar coordinates three comma pyro for that's r equals three and B equals power for and we want Teoh Express this in the Cartesian coordinates. So since we're given R and theta and we want to know except why we're gonna use our equations, X equals our coast. I'm Veda And why equals r sine theta says R and theta are on the right hand side. Readers plug in the values. So in the 1st 1 we have X equals three times co sign however, for which is three times, um, route to him or to cause and a partner for Israel to over to. And then, um Why equals three times sign of however for which is actually the same thing is sign of power for is also to or two um, so will it right? Are answer as a point. Um, so X is three years to over two can play. We can't simplify that anymore. And why is also 3 to 2? So any time the angle is pira Ford, you should expect, um X and y to be the same because that's that angle is on the line. Why was ex So there's our Cartesian coordinates
The point of coordinated appoint three by far they were given this only We aren't teatime here to convert into the captain's Ian. And then we have the X. We go to our own times. Course I Tita, why equals earn times under Tita, Therefore, x way could you treat him? Goes under point of far We're getting Kojic treat hymns cause a battle for coach you wonder was going to They were gonna treat on what's going on June and for the we're gonna treat them side of a parent for then we build something. The tree was good too. So this will be the boned three, almost with two and three and was quick up to
So remember that are squared is equal to X squared plus y squared. And if we have, if we have this equation than if we square both sides of the equation, we get R squared is equal to 16. And so we know how toe incorporate r squared, since our sport is just X squared plus y squared, and so this is equal to 16. So we have our rectangular equation. In other words, we have an equation that is in terms of X and y.
You a unit record for this sector. Oh, it's going to get its magnitude. And that's going to be equal to the square root of 16 plus nine. That's just fine. Okay? And then they also want a straight director and pulling for him. So we're bringing in big attention. Inverse. Ah, negative. 3/4. I'd see on angle Dennis. That should be tension and negative. Three. The writer before that's about negative. 0.64 Etienne's polar farm is being multiply the magnitude by coastline of your angle and sign of you know. Okay, so if we were data be that then polar form, it is fine co signed it a sign that awesome.