How do you convert the polar equation #theta=45^o# into rectangular form?

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Answer 1 · 2016-10-31T16:09:32

Questions of the "How do you" type are best answered by explanation. Please see below.

Given:

#theta = 45°#

Substitute #tan^-1(y/x)# for #theta# but add the restriction #x > 0 and y > 0 #

#tan^-1(y/x) = 45°; x > 0 and y > 0 #

Take the tangent of both sides:

#tan(tan^-1(y/x)) = tan(45°);x > 0 and y > 0 #

The tangent of its inverse returns #y/x# and #tan(45°) = 1#

#y/x = 1;x > 0 and y > 0 #

Multiply both sides by x and drop the restriction for y, because y is now dependent on x:

#y = x;x > 0#