Find two other pairs of polar coordinates of the given polar coordinate, one with r > 0 and one with r < 0.?
(3, 7π/6) and (-3, π/6)
Find two pairs of polar coordinates, one with r>0 and r<0. Express the angles in radians. (1, -1)?
Not quite. Your second angle is wrong. |r| = √2, you're right about that. So what you want is the simple solution: ( √2 , -π/4 ) Now you want another solution: ( -√2 , ? ) But here you want an angle opposite -π/4. To get that angle, you add π (half rotation) π - π/4 = 3π/4 So your answer is: ( √2 , -π/4 ) ( -√2 , 3π/4 )
Finding polar coordinates??
For a) add 2pi to -3pi/4 as many times as needed until 2pi
Plot the points whose polar coordinates are given Then find two other pairs of polar coordinates of this point?
Plot the point whose polar coordinates are given. (Do this on paper. Your instructor may ask you to turn in this work.) Then find two other pairs of polar coordinates of this point that match the conditions. (-3, π/6) (r > 0, 2π < θ ≤ 4π) I'm not sure why my answer is wrong with (3, 7π/6) the home work is due 6 hours from now.
Can r be negative in polar coordinates?
A point P in polar coordinates is specified using the pair of numbers (r,θ). Think of this as directions you need to reach point P while starting at the origin. You interpret these directions as follows,Stand at the origin facing the +x direction.If θ>0, turn left by an angle θ. If θ<0, turn right by an angle −θ. Do not turn at all if θ=0,If r>0, move forward r units. If r<0, move backward by −r units. If r=0, stay where you are,So it’s clear that it doesn’t matter whether r is negative or positive, it’s the interpretation of the position of the point that matters
For ( -2, -pi/3), find two other polar coordinates representations of the point, one with r<0, the other r>0.
if r >0 the angle is renamed by getting the opposite angle... add or subtract π thus (2, 2π/3) if r < 0 , get another coterminal of the angle... (-2,5π/3) §
How do I find alternative forms of a polar coordinate for a point?
Since polar coordinates involve a component of revolution, you can get multiple coordinates for each point by simply 'going around again.' Given a point (r, theta), we can write the point equivalently by (r, theta + 2n pi) for any integer n. You could also use ( - r, theta + n pi ) for odd integers. Hope this helps In degrees, you would use multiples of 180 instead of pi. (r, theta) = (r, theta + 360) = (r, theta + 360n) for any integer n or (r, theta) = (-r, theta + 180) = (r, theta + 180n) for n odd.
How do you find two pairs of coordinates for an equation by using a T-Chart in Algebra 2?
When you have a linear equation (straight line) like:y = x + 2To find the coordinates of a point on the line you use a T chart, giving a value to x and calculating the value of y:x ……. y-1 ….. 1 => (x, y) = (-1, 1)0 ….. 2 => (0, 2)1 …… 3 => (1, 3)And more as you wish.
In polar coordinates, every point has a unique ordered pair of coordinates to describe it?
false, you can describe any point but you can describe the same point in potentially infinite ways. example; the rectangular coordinate of (1,1) in polar you can describe this point as (pi/4,1) or (5pi/4, -1) and so on
Does polar coordinate have basis vectors?
Polar coordinates are not some linear combination of basis vectors.Polar coordinates (and Cartesian coordinates) are ways of mapping pairs of numbers to points on a plane. The plane, in this case, is not a vector space, so there are not necessarily any basis vectors.It is possible to associate a vector space with the plane, in which case you have a choice of bases to use, if you want to.For Cartesian coordinates, it is convenient to use unit vectors “aligned with” the cartesian axis as a basis. They are orthonormal, and it’s easy to calculate displacement vectors based on the coordinates.This isn’t so easy with polar coordinates.What is done, however, and generalizes to other coordinate systems, is to use the coordinates of a point to define a “natural” basis for an associated vector space at that point (theoretically, different points get different vector spaces). In which case, the basis vectors are tangent to the constant curves of the coordinate system (e.g., in polar coordinates, the basis at the point [math](r_0, \theta_0)[/math] has one vector tangent to the circle [math]r= r_0[/math], the the other vector tangent to the line [math]\theta = \theta_0[/math]).For a Cartesian coordinate system, all these different bases at each point is identical, so we don’t tend to think of it. For a polar coordinate system, they are all rotated compared to each other. It’s even convenient if they aren’t all unit vectors.Personally, I feel that there is confusion here because of two different uses of the word “coordinate”.