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# I have been trying to do my homework all day and i need help please and thank you

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The position of a particle is given by the parametric equations
as t ranges over all real numbers.

x=3+2sin(2t)

y=4+2cos(2t)

The particle visits the points P, Q, R, S at times -pi/6, 0, pi/3, pi/2 in some order. Order the points
so that the particle is at the first point at time -pi/6, at the second point at time 0, at the third point at time pi/3, and at the last point at time pi/2.

I would really appreciate an answer as soon as possible. Thanks!

Jul 26, 2024
edited by JRFPLSHelp  Jul 26, 2024

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P

x =   3 + 2sin (2 *-pi6)  =  3 + 2 sin (-pi/3)  = 3 + 2  *(-sqrt 3 / 2) = 3 - sqrt 3

y =    4 + 2cos (2 *-pi/6)  =  4 + 2 cos (-pi/3)  =   4 + 2(1/2) =  5

Q

x = 3 + 2sin (2*0)  = 3 + 2(0) =  3

y = 4 + 2cos (2*0) =  4 + 2 (1) = 6

R

x= 3 + 2sin (2 *pi/3) =  3 + 2 sin (2pi/3) = 3 + 2 (sqrt 3 / 2) =  3 + sqrt 3

y = 4 + 2cos(2 *pi/3) = 4 + 2 (-1/2) = 3

S

x = 3 + 2sin (2 *pi/2)  = 3 + 2 (0) =  3

y = 4 + 2cos (2 *pi/2)  = 4 + 2(-1) = 2

Jul 27, 2024