Converting the polar equation $r=12-sintheta+2sin3theta+2sin5theta-sin7theta+3cos2theta-2cos4theta$ to...
$begingroup$
How do I convert the following polar equation to rectangular equation?
$$r = 12 - sin(θ) + 2sin(3θ) + 2sin(5θ) - sin(7θ) +3cos(2θ) - 2cos(4θ)$$
polar-coordinates
edited Dec 6 '18 at 20:08
Blue
47.8k870152
asked Dec 6 '18 at 19:39
Venus P.Venus P.
11
$endgroup$
add a comment |
$begingroup$
How do I convert the following polar equation to rectangular equation?
$$r = 12 - sin(θ) + 2sin(3θ) + 2sin(5θ) - sin(7θ) +3cos(2θ) - 2cos(4θ)$$
polar-coordinates
edited Dec 6 '18 at 20:08
Blue
47.8k870152
asked Dec 6 '18 at 19:39
Venus P.Venus P.
11
$endgroup$
$begingroup$
Try to expres in terms of $costheta$ and $sin theta$ only, then $x = r cos theta$ etc.
$endgroup$
– Damien
Dec 6 '18 at 19:47
add a comment |
$begingroup$
How do I convert the following polar equation to rectangular equation?
$$r = 12 - sin(θ) + 2sin(3θ) + 2sin(5θ) - sin(7θ) +3cos(2θ) - 2cos(4θ)$$
polar-coordinates
edited Dec 6 '18 at 20:08
Blue
47.8k870152
asked Dec 6 '18 at 19:39
Venus P.Venus P.
11
$endgroup$
How do I convert the following polar equation to rectangular equation?
$$r = 12 - sin(θ) + 2sin(3θ) + 2sin(5θ) - sin(7θ) +3cos(2θ) - 2cos(4θ)$$
polar-coordinates
polar-coordinates
edited Dec 6 '18 at 20:08
Blue
47.8k870152
asked Dec 6 '18 at 19:39
Venus P.Venus P.
11
edited Dec 6 '18 at 20:08
Blue
47.8k870152
asked Dec 6 '18 at 19:39
Venus P.Venus P.
11
edited Dec 6 '18 at 20:08
Blue
47.8k870152
edited Dec 6 '18 at 20:08
Blue
47.8k870152
edited Dec 6 '18 at 20:08
Blue
47.8k870152
47.8k870152
asked Dec 6 '18 at 19:39
Venus P.Venus P.
11
asked Dec 6 '18 at 19:39
Venus P.Venus P.
11
asked Dec 6 '18 at 19:39
Venus P.Venus P.
11
11
$begingroup$
Try to expres in terms of $costheta$ and $sin theta$ only, then $x = r cos theta$ etc.
$endgroup$
– Damien
Dec 6 '18 at 19:47
add a comment |
$begingroup$
Try to expres in terms of $costheta$ and $sin theta$ only, then $x = r cos theta$ etc.
$endgroup$
– Damien
Dec 6 '18 at 19:47
$begingroup$
Try to expres in terms of $costheta$ and $sin theta$ only, then $x = r cos theta$ etc.
$endgroup$
– Damien
Dec 6 '18 at 19:47
$begingroup$
Try to expres in terms of $costheta$ and $sin theta$ only, then $x = r cos theta$ etc.
$endgroup$
– Damien
Dec 6 '18 at 19:47
add a comment |
1 Answer
1
active
oldest
votes
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Hint #1: Use some of the sum-to-product reduction formulas, for instance $$sin x + sin y = 2 sin frac {x+y} 2 cos frac {x-y} 2$$ to reduce it to at most $4 theta$.
Hint #2: If you know that $x = r cos theta$ and $y = r sin theta$, can you establish the other identities? To wit: $x y = r^2 cos theta sin theta rightarrow 2 x y = 2 r^2 cos theta sin theta rightarrow 2 x y = r^2 sin 2theta rightarrow frac {2 x y} {r^2} = sin 2theta$, etc.
answered Dec 6 '18 at 20:22
bjcolby15bjcolby15
1,20611016
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add a comment |
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1 Answer
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active
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1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
Hint #1: Use some of the sum-to-product reduction formulas, for instance $$sin x + sin y = 2 sin frac {x+y} 2 cos frac {x-y} 2$$ to reduce it to at most $4 theta$.
Hint #2: If you know that $x = r cos theta$ and $y = r sin theta$, can you establish the other identities? To wit: $x y = r^2 cos theta sin theta rightarrow 2 x y = 2 r^2 cos theta sin theta rightarrow 2 x y = r^2 sin 2theta rightarrow frac {2 x y} {r^2} = sin 2theta$, etc.
answered Dec 6 '18 at 20:22
bjcolby15bjcolby15
1,20611016
$endgroup$
add a comment |
$begingroup$
Hint #1: Use some of the sum-to-product reduction formulas, for instance $$sin x + sin y = 2 sin frac {x+y} 2 cos frac {x-y} 2$$ to reduce it to at most $4 theta$.
Hint #2: If you know that $x = r cos theta$ and $y = r sin theta$, can you establish the other identities? To wit: $x y = r^2 cos theta sin theta rightarrow 2 x y = 2 r^2 cos theta sin theta rightarrow 2 x y = r^2 sin 2theta rightarrow frac {2 x y} {r^2} = sin 2theta$, etc.
answered Dec 6 '18 at 20:22
bjcolby15bjcolby15
1,20611016
$endgroup$
add a comment |
$begingroup$
Hint #1: Use some of the sum-to-product reduction formulas, for instance $$sin x + sin y = 2 sin frac {x+y} 2 cos frac {x-y} 2$$ to reduce it to at most $4 theta$.
Hint #2: If you know that $x = r cos theta$ and $y = r sin theta$, can you establish the other identities? To wit: $x y = r^2 cos theta sin theta rightarrow 2 x y = 2 r^2 cos theta sin theta rightarrow 2 x y = r^2 sin 2theta rightarrow frac {2 x y} {r^2} = sin 2theta$, etc.
answered Dec 6 '18 at 20:22
bjcolby15bjcolby15
1,20611016
$endgroup$
Hint #1: Use some of the sum-to-product reduction formulas, for instance $$sin x + sin y = 2 sin frac {x+y} 2 cos frac {x-y} 2$$ to reduce it to at most $4 theta$.
Hint #2: If you know that $x = r cos theta$ and $y = r sin theta$, can you establish the other identities? To wit: $x y = r^2 cos theta sin theta rightarrow 2 x y = 2 r^2 cos theta sin theta rightarrow 2 x y = r^2 sin 2theta rightarrow frac {2 x y} {r^2} = sin 2theta$, etc.
answered Dec 6 '18 at 20:22
bjcolby15bjcolby15
1,20611016
answered Dec 6 '18 at 20:22
bjcolby15bjcolby15
1,20611016
answered Dec 6 '18 at 20:22
bjcolby15bjcolby15
1,20611016
answered Dec 6 '18 at 20:22
bjcolby15bjcolby15
1,20611016
1,20611016
add a comment |
add a comment |
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$begingroup$
Try to expres in terms of $costheta$ and $sin theta$ only, then $x = r cos theta$ etc.
$endgroup$
– Damien
Dec 6 '18 at 19:47