- #1
vee6
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How to convert the -300 deg (minus 300 degree) to a radian?
A unit vector directed at -300 degrees is coterminal with a unit vector directed at 60 degrees, but the angles are not equal. You are not correct.vee6 said:-300 deg = 60 deg
am I correct?
if so
-300 deg = π/3 rad
is it correct?
rock.freak667 said:π rad is equivalent to 180 deg.
so 1 deg = π/180 rad
(π =pi if it does not come out too clearly)
vee6 said:So
-300 deg = -300*(pi/180) rad = -5/3 * pi * rad
Is it correct?
Yes. Also note that since, as above, -300 degrees is equivalent to 60 degrees, we have the -300 degrees is equivalent to 60(pi/180)= pi/3 radians (If you are using "*" to indicate multiplication, do NOT write "* rad"). This is true because one/3 complete revolution is 2pi radians and 2pi- 5/3 pi= (6/3- 5/3)pi= pi/3 so that -(5/3)pi radian is equivalent to pi/3 radians.vee6 said:So
-300 deg = -300*(pi/180) rad = -5/3 * pi * rad
Is it correct?
HallsofIvy said:Yes. Also note that since, as above, -300 degrees is equivalent to 60 degrees, we have the -300 degrees is equivalent to 60(pi/180)= pi/3 radians (If you are using "*" to indicate multiplication, do NOT write "* rad"). This is true because one[STRIKE]/3[/STRIKE] complete revolution is 2pi radians and 2pi- 5/3 pi= (6/3- 5/3)pi= pi/3 so that -(5/3)pi radian is equivalent to pi/3 radians.
HallsofIvy said:What Mandelbroth is saying is that -300 is NOT "equal" to 60 but that since 360- 300= 60, they are equivalent and have the same trig function values.
They are equivalent as angles, but they certainly are NOT equal. Try expanding sine or cosine in a Taylor series using only finitely many terms, and compare the results if you plug in -300 degrees vs. 60 degrees.SteveL27 said:There is no way to distinguish an angle of -300 degrees to one of 60 degrees.
jbunniii said:They are equivalent as angles, but they certainly are NOT equal. Try expanding sine or cosine in a Taylor series using only finitely many terms, and compare the results if you plug in -300 degrees vs. 60 degrees.
They won't be exactly equal with only finitely many terms.SteveL27 said:I didn't believe they would be different so I wrote a little program to test it out. If you plug pi/3 and -5pi/3 into the Taylor series for cosine, they start out wildly different for a few terms but both settle down to 1/2, good to 6 decimal places, after about 12 terms. That's not bad at all, and it contradicts what you claim.
Theoretically they are indistinguishable if you consider the points on the unit circle to which they correspond. But what about other curves? If I have a closed curve which has a winding number greater than 1, I can certainly distinguish between -300 and 60. See the animated example here: http://en.wikipedia.org/wiki/Winding_numberIf I handed you a piece of paper showing an angle of 60 degrees; and another piece of paper showing an angle of -300 degrees; how would you tell them apart?
jbunniii said:They won't be exactly equal with only finitely many terms.
jbunniii said:Theoretically they are indistinguishable if you consider the points on the unit circle to which they correspond. But what about other curves? If I have a closed curve which has a winding number greater than 1, I can certainly distinguish between -300 and 60. See the animated example here: http://en.wikipedia.org/wiki/Winding_number
I guess I don't see what your complaint was with HallsOfIvy's statement:SteveL27 said:The analogy I gave earlier is the distiction between saying:
a) The integers 1 and 6 are equivalent, mod 5, but they are not the same number.
b) The members of the integers mod 5, [1] and [5], are equal.
He is saying exactly the same thing as you are. -300 and 60 are not equal, but [-300] and [60] are, if we define the equivalence classes to indicate angles which correspond to the same point on the unit circle.What Mandelbroth is saying is that -300 is NOT "equal" to 60 but that since 360- 300= 60, they are equivalent and have the same trig function values.
jbunniii said:He is saying exactly the same thing as you are. -300 and 60 are not equal, but [-300] and [60] are, if we define the equivalence classes to indicate angles which correspond to the same point on the unit circle.
The formula for converting degrees to radians is: radians = (degrees * pi) / 180.
The value of pi is approximately 3.14159.
To convert -300 degrees to radians, we use the formula: radians = (-300 * pi) / 180. This results in approximately -5.23599 radians.
Radians are a unit of measurement used in mathematics and science that are more convenient for calculations involving angles and trigonometric functions. They are based on the radius of a circle, making them a more natural unit for these types of calculations.
Yes, negative degrees can be converted to radians. The resulting value will also be negative, indicating a clockwise rotation from the origin.