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Find tha coordinales ol Ihe poinl Pon (he crcumlerence of (he circle (Hinl Add x ad y-axes, assuming Ihal Iho angle IS In standard posilion )15O?Tha coordinales ol ...

Question

Find tha coordinales ol Ihe poinl Pon (he crcumlerence of (he circle (Hinl Add x ad y-axes, assuming Ihal Iho angle IS In standard posilion )15O?Tha coordinales ol P are (Type an ordered palr ; Simplily YouI answer wcluding any radicals

Find tha coordinales ol Ihe poinl Pon (he crcumlerence of (he circle (Hinl Add x ad y-axes, assuming Ihal Iho angle IS In standard posilion ) 15O? Tha coordinales ol P are (Type an ordered palr ; Simplily YouI answer wcluding any radicals



Answers

Write in simplest radical form the coordinates of each point $A$ if $A$ is on the terminal side of an angle in standard position whose degree measure is $\theta .$
$O A=9, \theta=150^{\circ}$

All right, But this one, the Cartesian points were asked to find given the distance at an angle. And this one is quite simple because your angle is 180 degrees, which is just 1/2 turn around the access. So if you start here, you make a 180 degree angle, you're gonna be over here. And so if I just go 0.5 along that access that I'm gonna have an X value of minus 0.5. And if I'm on the X axis from my wife, value is zero.

All right. So this one we have where it is 90 in our ray a six. And so we have to find the corner points of 91st. So we would have co sign 90 equals zero and sign 90 equals one. Because 90 it's here. And if we look at the corner points here, that was zero comma one because it's on the Y axis Marais. And so find those me cornets four align the equal six minutes angle equals 90 degrees. We would do six times close on 90 com 06 times sine 90. Well, we already know what co star 90 equals on what siren equals, so we substitute in. So this would be six time zero comus. Six times one, and they're from there. The new coordinates would be zero comma, six.

All right. So this problem, Mrs that are positive race. It's for in our angle is 45 degrees. And we want to know what are the coordinate points for that particular line? All right, so the first thing we have to know is okay if I have 45. Well, what this coast on 45 equal? What? The sign? 45 equal? Because that's the first thing we gotta note. So if that's the case, we're looking at cold side 45 day. If you use a unit circle charge that could help. You would find in the Courtney points of those. So cool. Some 45 is radical to over two and signed 45 is radical to to. Well, we want to find the quarter points of four. So we would take four and multiply that times close. I'm 45 comma towards I'm signed 45 to find any coordinates. All right, so we would take 4/1 8 multiply that times radical to or with you, And then we would say, pour over one again, and most of that approach you. So we multiply these. We can go from here to your dues and this to become one. And this becomes for we convict you and we could do the same thing over here. And so a new corner points would be too radical, too, How much she radical to. And that would be the coordinates. Four when a lot of equals four at the angle 45.


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