Please check my answers;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)
Let's go through each question and check the answers:
1. Which of the following is another representation of (-3, pi)?
- (3, 120 degrees)
- (3, 0 degrees)
- (-3, 0 degrees)
To represent (-3, pi), we need to convert the angle to degrees. Since pi radians is equal to 180 degrees, (-3, pi) is equivalent to (-3, 180 degrees).
So, the correct answer is (-3, 180 degrees). None of the given options match this representation.
2. Which is not a representation of (5, 150 degrees)?
- (-5, -30 degrees)
- (-5, 330 degrees)
- (5, 510 degrees)
To determine which option is not a representation of (5, 150 degrees), we need to check if the angle and magnitude match.
(5, 150 degrees) represents a point with a magnitude of 5 and an angle of 150 degrees.
By converting 330 degrees to positive degrees, we get (5, 330 degrees), which is a representation of (5, 330 degrees). So, this option is a valid representation.
By converting -30 degrees to positive degrees, we get (5, -30 degrees), which is a representation of (5, -30 degrees). So, this option is also a valid representation.
By converting 510 degrees to positive degrees, we get (5, 510 degrees), which is equivalent to (5, 510 - 360 = 150 degrees). So, this option is a valid representation too.
None of the given options are incorrect representations. Therefore, the answer is none of the options.
3. Give 3 representations of (3, 240 degrees). One has to be in radians.
- (3, 600 degrees)
- (3, -120 degrees)
- (-3, pi/3)
To find the representations of (3, 240 degrees), we need to consider the equivalent angles.
Adding 360 degrees to 240 degrees:
- (3, 600 degrees) is equivalent to (3, 240 degrees).
Subtracting 360 degrees from 240 degrees:
- (3, -120 degrees) is equivalent to (3, 240 degrees).
In radians, pi is equal to 180 degrees. Therefore,
- (-3, pi/3) is equivalent to (-3, 240 degrees).
All three representations are correct.
4. Give 3 representations of (-6, 3pi/4). One has to be in radians.
- (-6, 495 degrees)
- (-6, -225 degrees)
- (6, -pi/4)
To find the representations of (-6, 3pi/4), we need to consider the equivalent angles.
Adding 360 degrees to 3pi/4:
- (-6, 495 degrees) is equivalent to (-6, 3pi/4).
Subtracting 360 degrees from 3pi/4:
- (-6, -225 degrees) is equivalent to (-6, 3pi/4).
In radians, pi is equal to 180 degrees. Therefore,
- (6, -pi/4) is equivalent to (-6, 3pi/4).
All three representations are correct.
In summary:
1. (-3, pi) is represented as (-3, 180 degrees).
2. None of the given options is not a representation of (5, 150 degrees).
3. (3, 240 degrees) can be represented as (3, 600 degrees), (3, -120 degrees), and (-3, pi/3).
4. (-6, 3pi/4) can be represented as (-6, 495 degrees), (-6, -225 degrees), and (6, -pi/4).
Let's go through your answers step-by-step:
1. The correct representation of (-3, pi) is (3, 0 degrees). You are correct.
2. The representation (-5, -30 degrees) is not equivalent to (5, 150 degrees). Therefore, you are correct in choosing it as the answer.
3. The three representations of (3, 240 degrees) are:
a. (3, 600 degrees) - This is correct.
b. (3, -120 degrees) - This is correct.
c. (-3, π/3 radians) - This is also correct.
So, all three of your choices are correct.
4. The three representations of (-6, 3π/4 radians) are:
a. (-6, 495 degrees) - This is correct.
b. (-6, -225 degrees) - This is also correct.
c. (6, -π/4 radians) - This is also correct.
All three of your choices are correct.
Overall, your answers are correct for all the questions. Well done!