Question

how would I solve this? x = 5 sin t, y = 5 cos t

Answer 1

you want to eliminate 't' ?
just square and add them

Answer 2

square them and add

Answer 3

sin^2t+cos^2t=1
trigonometry formula

Answer 4

so i sq them both?

Answer 5

wait what?

Answer 6

yes
find
x^2
and
y^2

Answer 7

\(x =5 \sin t \\ x^2 = (5 \sin t)^2 = ... ?\)

Answer 8

ok 25 sin^2 but how do i add them

Answer 9

y^2 = 25 cos^2 t

now add them

\( x^2 +y^2 = 25 \sin^2 t +25 \cos^2 t\)

what can you factor out ??

Answer 10

25 and t

Answer 11

note that
sin t and cos t are functions

and are not separate entities like 'sin' and 't'

so you cannot factor out t :)

Answer 12

just factor out 25 and see what u get

Answer 13

and use the fact that
\(
\sin^2 t + \cos^2 t =1\)

Answer 14

so it would be a circle

Answer 15

yes

Answer 16

what would be the radius of that circle ?

Answer 17

5

Answer 18

but what does this mean: Eliminate the parameter t from the following.

Answer 19

It means to do what you just did.
you now have
x^2 + y^2 = 5^2
no t !

Answer 20

no cos or sin?

Answer 21

no 't'

Answer 22

eliminate 't' means combine the equations in such a way that the new equation does not have the variable 't' at all

Answer 23

so the answer looks like this 5sin^2 +5cos^2

Answer 24

no

Answer 25

geez i dont get it

Answer 26

\(\sin^2 t +\cos^2 t\)
is already 1

Answer 27

oh yeah

Answer 28

25 (sin^2 t + cos^2 t) = 25*1 =25

Answer 29

25 (sin^2 t + cos^2 t) = 25

Answer 30

thats what they are asking for?

Answer 31

I think they are asking for you to change
x = 5 sin t, y = 5 cos t
into
x^2 + y^2 = 25

Answer 32

^^

Answer 33

the first form
x = 5 sin t, y = 5 cos t
is "parametric form"

you can calculate (x,y) pairs for values of "t"

the other form
x^2 + y^2 = 25
has no "t". You can still find (x,y) pairs, but it is a bit more painful

Answer 34

thank you so much thanks for your brilliance

Answer 35

If you want more background, see
https://www.khanacademy.org/math/precalculus/parametric_equations
and look at the first video in each section.

Answer 36

will do

Answer 37

and the 3rd video in the first section looks close to your problem
https://www.khanacademy.org/math/precalculus/parametric_equations/parametric/v/parametric-equations-3

The first 2 videos talk about the parametric form... which is useful if the idea is new.

Answer 38

well i am stuck on a another problem if you guys are up for the challenge

Answer 39

Find all solutions if
0 ≤ x < 2π.
Use exact values only. (Enter your answers as a comma-separated list.)
sin x cos 2x + cos x sin 2x = 1/2