Please check my answers I really need to do my homeowrk!;This are polar coordinates we're studying-I'm almost positive the first two are correct.
1.Which of the folowing is another representation of (-3,pi)?
(3,120degree)
(3,0 degree)I think it is this one??
((-3,0 degree)
2.Which is not a representation of (5,150 degree)
(-5,-30 degree)I think it is this one?
(-5,330 degree)
(5,510 degree)
3.Give 3 representations of (3,240 degree)One has to be in radians
My choices are: (3,600 degrees)
(3,-120 degree degree)
(-3,pi/3)
4.Give 3 representations of (-6,3pi/4)one has to be radians
I gave-(-6,495 degrees)
(-6,-225 degrees)
(6,-pi/4)
1. (-3,pi) = -3cos(pi) + i(-3)sin(pi) =
3 + io = 3.
(3,120deg) = -1.5 + i2.6
(3,0deg) = 3 + i0 = 3.
(-3,0deg) = -3 + i0 = -3.
2. (5,150deg) = -4.33 + i2.5
(-5,-30deg) = -4.33 + i2.5
(-5,330deg) = -4.33 + i2.5
(5,510deg) = -4.33 + i2.5
My calculations show that all of # 2 is
identical.
3. (3,240deg) = -1.5 - i2.6
(3,600deg) = -1.5 - i2.6
(3,-120deg) = -1.5 - i2.6
(-3,pi/3) = -1.5 - i2.6
Good!!
4. (-6,3pi/4) = 4.24 - i4.24
(-6,495deg) = 4.24 - i4.24
(-6,-225deg) = 4.24 -i4.24
(6,-pi/4) = 4.24 - i4.24.
Very good!
1. Which of the following is another representation of (-3, pi)?
- The correct answer is (-3, 0 degrees).
2. Which is not a representation of (5, 150 degrees)?
- The correct answer is (-5, 330 degrees). Good job!
3. Give 3 representations of (3, 240 degrees). One has to be in radians.
- The correct representations are:
1. (3, -120 degrees)
2. (-3, 4π/3 radians)
3. (3, 240 degrees) - This is the same as the original representation.
4. Give 3 representations of (-6, 3π/4). One has to be in radians.
- The correct representations are:
1. (-6, 135 degrees)
2. (-6, 7π/4 radians)
3. (6, -5π/4 radians)
You did a great job on your answers! Keep up the good work!
Let's go through each question and check your answers:
1. Which of the following is another representation of (-3, pi)?
- (3, 120 degrees)
- (3, 0 degrees)
- (-3, 0 degrees)
To convert from polar coordinates to rectangular coordinates, we use the following formulas:
x = r * cos(theta)
y = r * sin(theta)
For (-3, pi), we have:
x = -3 * cos(pi) = -3 * (-1) = 3
y = -3 * sin(pi) = -3 * 0 = 0
Therefore, the correct answer is (-3, 0 degrees).
2. Which is not a representation of (5, 150 degrees)?
- (-5, -30 degrees)
- (-5, 330 degrees)
- (5, 510 degrees)
Again, we use the formulas for rectangular coordinates:
x = r * cos(theta)
y = r * sin(theta)
For (5, 150 degrees), we have:
x = 5 * cos(150 degrees) = 5 * (-√3/2) ≈ -4.33
y = 5 * sin(150 degrees) = 5 * (1/2) = 2.5
From the options, (-5, -30 degrees) is not a correct representation as the x-coordinate should be positive, not negative.
3. Give 3 representations of (3, 240 degrees). One has to be in radians.
- (3, 600 degrees)
- (3, -120 degrees)
- (-3, pi/3)
For (3, 240 degrees), we have:
x = 3 * cos(240 degrees) = 3 * (-1/2) = -1.5
y = 3 * sin(240 degrees) = 3 * (-√3/2) = -2.6
For (3, 600 degrees), we are given a full rotation, which brings us back to the same point.
For (3, -120 degrees), we get the negative of the y-coordinate.
For (-3, pi/3), we convert 240 degrees to radians by using the conversion factor: 180 degrees = pi radians. So, pi = 180 degrees.
Therefore, (-3, pi/3) represents the same point.
4. Give 3 representations of (-6, 3pi/4). One has to be in radians.
- (-6, 495 degrees)
- (-6, -225 degrees)
- (6, -pi/4)
For (-6, 3pi/4), we have:
x = -6 * cos(3pi/4) = -6 * (-√2/2) = 6√2/2 = 3√2
y = -6 * sin(3pi/4) = -6 * (√2/2) = -3√2
Therefore, the correct representation is (-6, -3√2) or (-6, -225 degrees).
You got most of the answers correct, good job! However, there were a couple of mistakes. Make sure to review the conversion formulas for rectangular and polar coordinates to avoid confusion.