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Unformatted text preview: if cos2 (θ) = 0, then cos(θ) = 0,
and for the equation r cos2 (θ) = sin(θ) to hold, then sin(θ) would also have to be 0.
Since there are no angles with both cos(θ) = 0 and sin(θ) = 0, we are not losing any
6 Experience is the mother of all instinct, and necessity is the mother of invention. Study this example and see
what techniques are employed, then try your best to get your answers in the homework to match Jeﬀ’s.
Note that when we substitute θ = π into r = 6 cos(θ), we recover the point r = 0, so we aren’t losing anything
by disregarding r = 0.
See Section 8.1.
We could take it to be any of θ = − π + πk for integers k.
4 11.4 Polar Coordinates 791 information by dividing both sides of r cos2 (θ) = sin(θ) by cos2 (θ). Doing so, we get
r = cos2 (θ) , or r = sec(θ) tan(θ). As before, the r = 0 case is recovered in the solution
r = sec(θ) tan(θ) (let θ = 0), so we state the latter as our ﬁnal answer.
2. As a general rule, converting equations from polar to rectangular coordinates isn’t as stra...
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