Question

Rewrite the parametric equations in Cartesian form: X(t) = -3sin t, y(t) = 3 cos t​

Answer 1

Hi the answer is 9sin ur welcome Hope this helps have a great day

Answer 2

`( (x)/(3) ) {}^(2) + ( (y)/(3)) {}^(2) = 1`

or x² +y²= 9

Explanation:

In Cartesian form, the equation is expressed only in terms of y and x.

x= -3sin(t) -----(1)

y= 3cos(t) -----(2)

I've written x instead of x(t) as in the later part of the working, we will be having an equation of only x and y, thus x will no longer be a function of t. This applies to equation 2, where I have replaced y(t) with y.

Relating sine to cosine:

sin²(t) +cos²(t)= 1

[sin(t)]² +[cos(t)]²= 1 -----(3)

From (1):

`(x)/( - 3) = \sin(t)`

`\sin(t) = - (x)/(3)` -----(3)

From (2):

`(y)/(3) = \cos(t)`

`\cos(t) = (y)/(3)` -----(4)

Substitute (4) &(5) into (3):

`( - (x)/(3) )^(2) + ( (y)/(3)) {}^(2) = 1`

`( (x)/(3) ) {}^(2) + ( (y)/(3) ) {}^(2) = 1`

The steps below are optional as the above is already considered to be the Cartesian form.

`\frac{ {x}^(2) }{9} + \frac{y {}^(2) }{9} = 1`

Multiplying both sides by 9:

x² +y²= 9