# Convert another equation x^2+y^2=4 to polar form

• MHB
• Elissa89
In summary, the polar equation for a circle centered at the origin is simply r=a, where a represents the radius of the circle.
Elissa89
x^2+y^2=4

I have so far:

(r^2)cos^(theta)+(r^2)sin(theta)=4

Idk what I'm supposed to do from here

You need to also square the trig. functions:

$$\displaystyle x^2+y^2=4$$

$$\displaystyle (r\cos(\theta))^2+(r\sin(\theta))^2=4$$

$$\displaystyle r^2\cos^2(\theta)+r^2\sin^2(\theta)=4$$

Factor the LHS...what do you have...is there a trig. identity you can apply?

MarkFL said:
You need to also square the trig. functions:

$$\displaystyle x^2+y^2=4$$

$$\displaystyle (r\cos(\theta))^2+(r\sin(\theta))^2=4$$

$$\displaystyle r^2\cos^2(\theta)+r^2\sin^2(\theta)=4$$

Factor the LHS...what do you have...is there a trig. identity you can apply?

got it! thanks!

Elissa89 said:
got it! thanks!

We see we have a circle centered at the origin, and in polar coordinates, that's simply a constant value for $$r$$. The Cartesian equation:

$$\displaystyle x^2+y^2=a^2$$ where $$0<a$$

Has the polar equation:

$$\displaystyle r=a$$

## 1. What is polar form for an equation?

Polar form is a way of representing complex numbers using their distance from the origin (known as the modulus) and the angle they form with the positive real axis (known as the argument).

## 2. How do I convert an equation in rectangular form to polar form?

To convert an equation from rectangular form (x + iy) to polar form (r(cosθ + isinθ)), you can use the following formulas: r = √(x² + y²) and θ = tan⁻¹(y/x).

## 3. What does x^2+y^2=4 look like in polar form?

In polar form, the equation x^2+y^2=4 can be written as r=2, which is a circle with radius 2 centered at the origin.

## 4. Why is it useful to convert equations to polar form?

Converting equations to polar form can make it easier to visualize and understand their geometric properties. It also allows for simpler calculations when working with complex numbers.

## 5. Can any equation be converted to polar form?

Not all equations can be converted to polar form. Only equations that involve the variables x and y and have a power of 2 can be converted. Additionally, some equations may have simpler forms in rectangular form compared to polar form.

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