How do you find the points of intersection of #r=3+sintheta, r=2csctheta#?

Answer 1

Polar coordinates of points of intersection are #(3.56,34.16^@)# and #(3.56,145.84^@)#

Point of intersection of #r=3+sintheta# and #r=2csctheta#
will be given by #3+sintheta=2csctheta#
i.e. #3+sintheta=2/sintheta#
or #sin^2theta+3sintheta-2=0#
or #sintheta=(-3+-sqrt(3^2-4xx1xx(-2)))/2=(-3+-sqrt17)/2#
As #|sintheta|<=1#, #(-3-sqrt17)/2# is not permissible and hence
#sintheta=(-3+sqrt17)/2=0.5616# or #theta=34.16^@# or #180^@-34.16^@=145.84^@#
and #r=3+sintheta=3+(-3+sqrt17)/2=(3+sqrt17)/2~=3.56#
Hence, polar coordinates of points of intersection are #(3.56,34.16^@)# and #(3.56,145.84^@)#

These are depicted in rectangular coordinates as shown below. graph{(y-2)(x^2+y^2-y-3sqrt(x^2+y^2))=0 [-10, 10, -5, 5]}

Sign up to view the whole answer

By signing up, you agree to our Terms of Service and Privacy Policy

Sign up with email
Answer 2

To find the points of intersection of the polar curves ( r = 3 + \sin(\theta) ) and ( r = 2\csc(\theta) ), set them equal to each other: ( 3 + \sin(\theta) = 2\csc(\theta) ). Solve this equation for ( \theta ) to find the values of ( \theta ) where the curves intersect. Then, substitute these values of ( \theta ) back into either of the original equations to find the corresponding values of ( r ).

Sign up to view the whole answer

By signing up, you agree to our Terms of Service and Privacy Policy

Sign up with email
Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

Not the question you need?

Drag image here or click to upload

Or press Ctrl + V to paste
Answer Background
HIX Tutor
Solve ANY homework problem with a smart AI
  • 98% accuracy study help
  • Covers math, physics, chemistry, biology, and more
  • Step-by-step, in-depth guides
  • Readily available 24/7