What is the graph of this parametric equation? x = 6 sin t, y = 6 cos t; the domain: 0 ≤ t ≤ 2pi

Question

amorfide · Answer

you want to get the equations in terms of sint and cost

x=6sint

divide by 6

x/6=sint

y=6cost

divide by 6

y/6=cost

then you know that

$$\sin^{2}t+\cos^{2}t=1$$

so you square them both, and add them together to get


$$(\frac{ x }{ 6 })^{2} + (\frac{ y }{ 6 })^{2}= \sin^{2}t+\cos^{2}t$$

$$(\frac{ x }{ 6 })^{2} + (\frac{ y }{ 6 })^{2} = 1$$

anonymous · Answer

i'm following you so far, just not sure on the graphing

amorfide · Answer

since the domain for t was from 0<t<2pi
you know that it must be in all quadrants

you know

$$x^{2}+y^{2}=r^{2}$$ is a circle centre (0,0) radius r

since the x and y are divided by the same number, it will represent a circle

you could expand out the brackets if you prefer, and then you can surely draw a circle graph

anonymous · Answer

oh okay thank you!! that really cleared it up for me i understand now :)

amorfide · Answer

no problem I am glad I could help