- #1
Elissa89
- 52
- 0
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
I have so far:
(r^2)cos^(theta)+(r^2)sin(theta)=4
Idk what I'm supposed to do from here
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?
Elissa89 said:got it! thanks!
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).
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).
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.
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.
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.