A lattice point is a point with integer coordinates. How many lattice points (x,y) with -100 less than or equal to x less than or equal to 100 and -100 less than or equal to y less than or equal to 100 are on the graph of the parametric equations x=30-40 cos t

Question

y=-50 + 30 cos t ?

Guys, can someone please give me a step by step way to do this problem? I am very confused.

Thanks!!!!

Answer 1

eliminate t:

(30-x)/40 = (50+y)/30
30(30-x) = 40(50+y)
900-30x = 2000+40y
30x+40y = -1100
3x+4y = -110

x = 4n+2
y = -(3n+29)

Now just work out how many values of n produce x and y in the desired interval.

Answer 2

I think it is 9. Am I right?

Answer 3

It is saying it is wrong where have i messed this up?

Answer 4

well, let's see
n   x   y
23 94 -98
22 90 -95
...
-22 -86 37
-23 -90 40
-24 -94 43
-25 -98 46

Looks like a lot more than 9 to me.

Answer 5

Oops. Not all of those are on the graph. You may be right.

Answer 6

Actually, it's 21, to anybody out there who still needs this question answered.

Answer 7

Thank you Dr. Legit! that was very helpful