a circle of radius 5 centered at the point 2,1 and traced out counterclockwise
Stacey Warren - Expert brainly.com
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ok, what do you need to know about it?
x = 2 + 5cos(t)
y = 1 + 5sin(t)
where t is between 0 and 2π
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how did you come up with that can u please show me?
Circles are defined by the equation (x-a)^2 + (y-b)^2 = r^2 where (a, b) is the center and r is the radius.
i understand that you plugged in the points into the equation and you got (x-2)^2 + (y-1)^2 = 5^2 . i don't understand what happend next
Right. So if you remember that sin^2(x) + cos^2(x) = r^2 (a trig identity)
If we want to rewrite this in terms of parametric we want (x-2)^2 = sin^2(t) and (y-1)^2 = cos^2(t)
Solving each of these yields what I posted before and the 5 is just to factor for the radius.
can you please show me how u solved for one of them (cos)
The 5 is because if you want sin^2(t) + cos^2(t) [a trig identity that equals 1] to equal 25 (5^2) then you have to multiply the original equation by 25 so 25sin^2(t) + 25cos^2(t) = 5^2
(y-1)^2 = 25cos^2(t) so if you take the square root of both sides you'd get (y-1) = 5cos(t) and then adding 1 to both sides yields y = 1 + 5cos(t).
if it is counterclockwise should cos be equal to x
I think setting 0≤t≤2π handles the counterclockwise part (if you think about your unit circle this should make sense). I do know that parametric equations are not unique in that there are multiple ways to express the same shape with different parametric curves.