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Find the values of theta which satisfy r...

Find the values of `theta` which satisfy `r sin theta=3` and `r=4 (1 + sin theta), 0 <= theta <= 2 pi`

Text Solution

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We have
`r sin theta =3` and `r=4 (1+ sin theta)`
Eliminating r, we get
`4 sin^(2) theta +4 sin theta -3 =0`
`:. (2 sin theta-1) (2 sin theta +3)=0`
`rArr sin theta =1/2, -3/2` (not possible)
`rArr theta=pi/6, (5 pi)/6`
Thus, we have two solutions.
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