How do you convert 5x-8y=7 into polar form ?

Question

1579 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-05-15T15:23:44

# r = 7/(5costheta - 8 sin theta ) #

Use our conversions:

# x = rcostheta #

#y = r sin theta #

#=> 5rcostheta - 8 r sin theta = 7 #

#=> r ( 5costheta - 8 sin theta ) = 7 #

#=> r = 7/(5costheta - 8 sin theta ) #

Answer 2 · 2018-05-15T15:53:39

The answer is:
#r = 7/(5costheta-8sintheta)#

Here is a simple polar graph:
enter image source here

We can derive some expressions from the graph, such as:

#sintheta = y/r, #i.e. #y = rsintheta# ..............(1)
#costheta = x/r,#i.e.#x = rcostheta# ..............(2)

Now the given equation is:

#5x-8y = 7#

Let's substitute the values of #x# and #y# from #(1)# and #(2)#, we get:

#5(rcostheta) - 8(rsintheta) = 7#
#or, r(5costheta-8sintheta)=7#
#or,r = 7/(5costheta-8sintheta)# .................(Answer)

**Hope this was Helpful