circular sector
- Thread starter xdem713o
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mmm4444bot
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xdem713o said:
We can't divide just one side of an equation by 4.5 !
Also, since you're trying to solve for O, you need to divide both sides by 2.5, not 4.5.
mmm4444bot
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I can't read your mind; I can only go by the words that you type.
Here's what you typed:
?
xdem713o said:
xdem713o said:
If you're not able to understand the contradiction, then I cannot help you.
Why do you think O = 1.8 radians is wrong?
D
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xdem713o said:
When you said "... I know that this isn't the answer" --- how did you know that?
When you use S = rO --- what is the unit of "O"?
xdem713o said:
I assume you are using O to represent "theta."
I'll use @ for theta....
s = r*@
You need to understand that in this formula, @ (theta) is the measure of the central angle in radians.
Now, you are given values for s and r. Both are in the same units, so you can substitute those values into the formula:
4.5 = 2.5*@
As previous responses have indicated, you need to divide both sides by 2.5 to get @ by itself.
4.5/2.5 = (2.5 @)/2.5
1.8 = @
So, the central angle has a measure of 1.8 RADIANS.
Why do you think that is incorrect? If you can explain that, we could probably help you "straighten out" your thinking.
The only reason I thought 1.8 radians was wrong is bc the answer key in the back of the book says that the answer is 103.1 degrees. And then I said "oh maybe the 1.8 rad. has to be converted to degrees, so I multiplied (1.8 rad) (360 degrees/ 2 pi rad) and I got 324 degrees.
You're thinking about converting radians to degrees is correct - you're almost done.
You said:
"so I multiplied (1.8 rad) (360 degrees/ 2 pi rad) and I got 324 degrees"
So you are stating the calculation:
\(\displaystyle \frac{1.8\; rad}{1}\cdot\frac{360\; degrees}{2\pi\; rad}\)
Double check your calculation - did you divide out \(\displaystyle \pi\) ?
You said:
"so I multiplied (1.8 rad) (360 degrees/ 2 pi rad) and I got 324 degrees"
So you are stating the calculation:
\(\displaystyle \frac{1.8\; rad}{1}\cdot\frac{360\; degrees}{2\pi\; rad}\)
Double check your calculation - did you divide out \(\displaystyle \pi\) ?
mmm4444bot
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xdem713o said:
Hi xDEM:
I just noticed that this exercise does specifiy reporting angle O's measurement in degrees. I regret that I missed that specification, after focusing on the other issues in your work shown, because I would have actually worked the entire exercise before responding.
The formulas that relate angular velocity, linear velocity, and arc length all depend upon working with angles in radian measure. In other words, when you see the symbol ? in a formula, you need to remember that it always represents some number of radians -- unless it's accompanied by some statement explicitly defining the units as degrees.
Here's the standard notation:
If some angle is stated as 30, then it must be assumed that the angle measure is 30 radians.
If some angle is stated as 30°, then it's clear that the angle measure is 30 degrees.
If some angle is stated as ?, then it must be assumed that the angle measure is in radians.
If someone uses the greek letter Theta to represent an angle's measure in degrees, then they are responsible for writing it as ?°.
Be forewarned, there are many sloppy educators and textbook authors who fail to follow this standard.
Again, if you don't explicitly see the degree symbol ° in an exercise (or the word "degrees" spelled-out), then proceed on the basis that you're working with radians.
s = r * ? means the angle must be measured in radians.
? = ?/t means the angle must be measured in radians.
I feel somewhat badly that I snapped at you because (at the time) I didn't realize the actual issue in this discussion.
Cheers ~ Mark
