Question

I need to turn, 4 divided by 8 cosine theta plus 5 sine theta, into terms of x and y. please help me.

Answer 1

\[(4)/(8\cos(\theta)*5\sin(\theta))\]

Answer 2

I am in precalculus right now. and that equation i wrote is supposed to be 8costheta plus 5sintheta. sorry.

Answer 3

is this a polar equation?

Answer 4

r = 4 / ( 8 cos t 5 sin t ) ?

Answer 5

yes it is!

Answer 6

so you can simplify this

r = 4 / ( 8 cos t 5 sin t )
r = 4 / ( 40 cos t sin t )

multiply both sides by 40 cos t sin t

r * 40 cos t sin t = 4

multiply both sides by r

r * r * 40 cos t sin t = 4 r

40 * (r cos t)( r sin t) = 4 r

40 * x * y = 4 sqrt( x^2 + y^2)

Answer 7

Thank You!

Answer 8

Well that's why I asked earlier if calculus could be used :P Haha didn't know you used polar coordinates in Pre calc, must've forgotten :(

Answer 9

@perl - I think that the equation to convert was supposed to be:\[r=\frac{4}{8\cos(\theta)+5\sin(\theta)}\]

@Calenk - divide both sides by \(r\) to get:\[1=\frac{4}{r(8\cos(\theta)+5\sin(\theta))}=\frac{4}{8r\cos(\theta)+5r\sin(\theta)}\]
Then
Now use the fact that:\[x=r\cos(\theta)\]\[y=r\sin(\theta)\]
Hopefully you can solve the rest

Answer 10

yours is right anseer