Determine two pairs of polar coordinates for the point (2, -2) with 0° ≤ θ < 360°.?

3 Answers

• given: point (x = 2, y = -2) with 0° ≤ θ < 360°

  polar coordinate equations:

  x = r cos(θ)

  y = r sin(θ)

  or

  2 = r cos(θ)

  -2 = r sin(θ)

  dividing we have

  tan(θ) = r sin(θ) / (r cos(θ)) = -2 / 2 = -1

  or θ = 315

  hence to find the radius r

  2 = r cos(θ)

  2 = r cos(45)

  r = 2 / cos(45)

  r = 2 / (1 / sqrt(2))

  r = 2 sqrt(2)

  hence one point is:

  (r = 2 sqrt(2) , θ = 315°)

  another point is:

  (r = -2 sqrt(2) , θ = 135°)

• a million) Polar coordinates are given with 2 coordinates: the perspective of the line between the element to the beginning from the x-axis; and the dimensions of that line. although, you additionally can supply the complementary perspective, with a damaging sign. this is sparkling in case you seem at a graph that, because (5,-5) bisects the fourth quadrant, the perspective is 40 5 stages. additionally, because of the fact the line is the hypotenuse, and a=b=5, we see that 25 + 25 = c*c = 50 = 25 * 2 . for this reason c = 5*Sqrt(2). So this is the two (7*40 5, c) or (-40 5, c) 2) right here we would desire to apply arcsin or arccos. So this is ( variety(5*5 + pi/3 * pi/3) =c - arcsin ( pi/3 / c)

• (2,-2) is in the 4th quadrant,

  so what's needed is a positive radius with theta=315 degrees

  or a negative radius with theta=135 degrees.

  Choice #3.