Question

In: Advanced Math

1. Find a Cartesian equation for the curve. r cos(θ) = 2 Identify the curve. 2....

1. Find a Cartesian equation for the curve.

r cos(θ) = 2

Identify the curve.

2. Find a Cartesian equation for the curve.

r = 4 sin(θ)

Identify the curve.

Expert Solution

The above diagram shows the polar as well as Cartesian coordinates of a point P. The rectangle OAPB shows that AP=OB=y, OA=BP=x, OP=r. Then, by trigonometry on triangle OAP,

,.

1)

Now, the equation given is , and we know . So, the Cartesian equation is x=2, which is the straight line passing through (2,0) and parallel to the y axis.

2)

Now, the equation given is . Now, ...(A)

Now,

Then, from (A):

,

So, the Cartesian equation of the given polar equation is , which is the circle of radius 2, centred at (0,2).

Colby Messinger answered 1 year ago

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