Please check:
1.Find polar equation of x^2 + y^2 = 10y
r^2 for x^2 + y^2 and sin(theta sin for y
=r^2=10sin(theta)
2.Find polar equation:
y=5
r=5/sin
3.Polar equation is r=2costheta + 3 sin theta
Find rectangular equation
x^2+y^2 =x^2 + y^2 =2x+3y
Jeez! How many times?
(3x5+4x4+4x3-3):(3x3+x2-1)
1. To find the polar equation of the given equation x^2 + y^2 = 10y, we need to convert it into polar form using the relations x = rcos(theta) and y = rsin(theta).
Start by substituting the values of x and y into the equation:
(r*cos(theta))^2 + (r*sin(theta))^2 = 10(r*sin(theta))
Simplify the equation:
(r^2*cos^2(theta)) + (r^2*sin^2(theta)) = 10r*sin(theta)
Apply the trigonometric identity cos^2(theta) + sin^2(theta) = 1:
r^2*(cos^2(theta) + sin^2(theta)) = 10r*sin(theta)
Substitute 1 for (cos^2(theta) + sin^2(theta)):
r^2*1 = 10r*sin(theta)
Simplify the equation:
r^2 = 10r*sin(theta)
Therefore, the polar equation for x^2 + y^2 = 10y is r^2 = 10r*sin(theta).
2. The given equation y = 5 can be directly converted into polar form. The equation represents a horizontal line y = 5, which corresponds to a circle with radius 5 units at a distance of 5 units from the origin.
In polar form, the equation becomes r = 5/sin(theta).
3. To convert the polar equation r = 2cos(theta) + 3sin(theta) into rectangular form, we need to use the relationships x = rcos(theta) and y = rsin(theta).
Substitute the values of x and y into the equation:
x^2 + y^2 = (2cos(theta) + 3sin(theta))^2
Expand the equation:
x^2 + y^2 = 4cos^2(theta) + 12cos(theta)sin(theta) + 9sin^2(theta)
Apply the trigonometric identity cos^2(theta) + sin^2(theta) = 1:
x^2 + y^2 = 4 + 12cos(theta)sin(theta) + 9
Simplify the equation:
x^2 + y^2 = 13 + 12cos(theta)sin(theta)
Therefore, the rectangular equation for the polar equation r = 2cos(theta) + 3sin(theta) is x^2 + y^2 = 13 + 12cos(theta)sin(theta).