Which of the following is NOT the same point in polar coordinates as (3, -1.236)? (-3, 1.906) (3, -7.518) (3, 5.047) (-3, 1.236)

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Which of the following is NOT the same point in polar coordinates as (3, -1.236)? (-3, 1.906) (3, -7.518) (3, 5.047) (-3, 1.236)

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Answer 1 · 2017-12-15T21:32:34

$(- 3, 1.236)$ $(-3, 1.236)$

Explanation:

Given:

$(3, - 1.236)$ $(3, -1.236)$

$(- 3, 1.906)$ $(-3, 1.906)$

$(3, - 7.518)$ $(3, -7.518)$

$(3, 5.047)$ $(3, 5.047)$

$(- 3, 1.236)$ $(-3, 1.236)$

Note that:

$7.518 - 1.236 = 6.282 \approx 2 π$ $7.518-1.236 = 6.282 ~~ 2pi$

$5.047 + 1.236 = 6.283 \approx 2 π$ $5.047+1.236 = 6.283 ~~ 2pi$

$1.236 + 1.906 = 3.142 \approx π$ $1.236+1.906 = 3.142 ~~ pi$

If the sign of $r$ $r$ is inverted, then to get the same point you need the signs of $cos θ$ $cos theta$ and $sin θ$ $sin theta$ to both be inverted. This can be done by replacing $θ$ $theta$ with $θ + π$ $theta+pi$

$sin$ $sin$ and $cos$ $cos$ both have period $2 π$ $2pi$ .

So we can tell:

The first and second coordinates are equivalent, since $1.906 \approx - 1.236 + π$ $1.906 ~~ -1.236+pi$ and the sign of $r$ $r$ is inverted.
The first and third coordinates are equivalent, since the $θ$ $theta$ values differ by $2 π$ $2pi$ .
The first and fourth coordinates are equivalent, since the $θ$ $theta$ values differ by $2 π$ $2pi$ .
The fifth coordinates are not equivalent: Inverting the signs of $r$ $r$ and $θ$ $theta$ does not generally give the same point.

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Which of the following is NOT the same point in polar coordinates as (3, -1.236)? (-3, 1.906) (3, -7.518) (3, 5.047) (-3, 1.236)

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Explanation:

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