Question

Write the following polar equations in rectangular form:\[a.)~r=2sin\theta-2cos\theta\]\[b.)~r=5sin\theta\]\[c.)~r-3sin\theta+4cos\theta\]

Answer 1

@jim_thompson5910

Answer 2

r = 2*sin(t) - 2*cos(t)


r*r = r*(2*sin(t) - 2*cos(t)) ... multiply both sides by r


r*r = 2*(r*sin(t)) - 2*(r*cos(t)) ... distribute and regroup


r*r = 2*(r*sin(t)) - 2*(x) ... use the identity x = r*cos(t)


r*r = 2*(y) - 2*(x) ... use the identity y = r*sin(t)


r^2 = 2y - 2x


x^2 + y^2 = 2y - 2x ... use the identity r^2 = x^2 + y^2


x^2 + 2x + y^2 - 2y = 0


x^2 + 2x + 1 + y^2 - 2y + 1 = 1 + 1


(x + 1)^2 + (y - 1)^2 = 2

Answer 3

so

r = 2*sin(t) - 2*cos(t)

turns into

(x + 1)^2 + (y - 1)^2 = 2

which is a circle centered at (-1, 1) and has a radius of sqrt(2) units

Answer 4

ohhh okay i remember how to do it now :D

Answer 5

r = 5*sin(t)

r*r = r*(5*sin(t))

r^2 = 5*(r*sin(t))

r^2 = 5y

x^2 + y^2 = 5y

x^2 + y^2 - 5y = 0

x^2 + y^2 - 5y + 25/4 = 25/4

x^2 + (y-5/2)^2 = 25/4

circle with center (0,5/2) and radius 5/2

Answer 6

ok great

Answer 7

thanks jim :)

Answer 8

np