plc function mean

plese talk me
what diferance in Arc sin, arc tan and sin , tan function

Walkslow first! (ps Google is your friend)

runfast said:

plese talk me
what diferance in Arc sin, arc tan and sin , tan function

Click to expand...

That is a good question and I would like to understand more about this from an engineer who works with them all the time.

I am forced by Excel to use arc sin and other trig functions in this format but do not understand why they are any better than the Lotus version where one could just use sin and get a value. I can eventually get Excel to do what I want with trig but have to read the manual every time I do it - which is not frequent.

I also do not comprehend why radians are valuable. I know that they are used to get away from degrees and start with a number ie 2piR = 360. But what I do not comprehend is why that is any better than 360/360 (one rev) or 180/360 (one half rev).

Dan Bentler

radian is the SI unit of angle. Classic example is

Power(W) = Torque(Nm) * Speed(rad/sec)

I work with them all the time.

leitmotif said:

I also do not comprehend why radians are valuable.

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Look at the Wikipedia link that Bob O posted. Midway down there is a series definition. This is the formula that computers use to compute sines and cosines. The x is these series function is in radians, not degrees. That is why radians are used. One could make a 'special' version that uses degrees but that would complicate things in the function itself. For one thing the numbers would get bigger faster leading to resolution problems more quickly although is not as big as problem now with 80bit reals. I think I have seen some basics language version that used degrees but real mathematicians use radians.

A version that used degrees would look like
sin(d)=d/(2∏)-(d/(2∏))^3/3!+(d/(2∏))^5/5!-(d/(2∏))^7/7!
to optimize this one can combine the factorial and 2∏ terms. The seventh order denominator would be 1.95x10^9 instead of 5040. That is a big difference and a CPU with 32 bit floats would suffer from a loss of precision.

leitmotif said:

I am forced by Excel to use arc sin and other trig functions in this format but do not understand why they are any better than the Lotus version where one could just use sin and get a value.

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I do not think this was the meaning of the original question.

leitmotif said:

I also do not comprehend why radians are valuable. I know that they are used to get away from degrees and start with a number ie 2piR = 360. But what I do not comprehend is why that is any better than 360/360 (one rev) or 180/360 (one half rev).

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Unlike human-introduced arbitrary 360 degrees per circle, Radian has strong physical meaning. It is the angle of circle sector with arc length equal to the radius.

Peter Nachtwey said:

Look at the Wikipedia link that Bob O posted. Midway down there is a series definition. This is the formula that computers use to compute sines and cosines. The x is these series function is in radians, not degrees. That is why radians are used. One could make a 'special' version that uses degrees but that would complicate things in the function itself. For one thing the numbers would get bigger faster leading to resolution problems more quickly although is not as big as problem now with 80bit reals. I think I have seen some basics language version that used degrees but real mathematicians use radians.

A version that used degrees would look like
sin(d)=d/(2∏)-(d/(2∏))^3/3!+(d/(2∏))^5/5!-(d/(2∏))^7/7!
to optimize this one can combine the factorial and 2∏ terms. The seventh order denominator would be 1.95x10^9 instead of 5040. That is a big difference and a CPU with 32 bit floats would suffer from a loss of precision.

Click to expand...

Peter I like to think of myself as a real mathemitician not an unreal one. The problem for me is radians were introduced to me in a college calculus course, the course was very fast running and I have not had the need for calculus since. It is only recently I have seen any need to scrape the rust off what little I learned in calculus class with respect to radians.

Much of my work in math is often done on paper where I need no high degree of precision 5 or 10% suffices. So simple trig (Suzy Can Tell,,,,) suffices for my needs. Where things get a bit more complicated I use a computer whose values are verified by pencil and paper, inserting a value whose result I know or judgement.

Looked at web page referred to in previous post.
The one problem I now see with my theory of just divide degrees by 360 is there is no negative value when either x or y go negative. Now that I see that error in thinking the learning proceeds.

Dan Bentler

When is your homework due? What class is this being used in?

OZEE said:

When is your homework due? What class is this being used in?

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self teach 101. Poor instructor but the tuition is sure right.

Dan Bentler

Dan, just be happy you don't have to use gradians.

To sum it up: although measuring angles in radians does not seem as intuitive as measuring in degrees, a lot of calculations end up in a much simpler and manageable form.

Degrees are just a human habit, hailing back as far as ancient Sumerians and Babylonians, but it is no less an arbitrary way to measure angles as would be any other. Why not split a full circle into 100 pieces? Or 1000? Well, the ancients thought there was 360 days in a year so they just split the celestial Sun circle in 360 pieces - one per day. It stuck.

With radians, the length of an arc segment becomes a simple product of the angle value and the radius. A full circle? 2*pi radians; a half-circle? just pi. A right angle? pi/2 - and so on.

Alaric said:

Dan, just be happy you don't have to use gradians.

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Uhhh value for slope - correct?


Dan

LadderLogic said:

To sum it up: although measuring angles in radians does not seem as intuitive as measuring in degrees, a lot of calculations end up in a much simpler and manageable form.

Degrees are just a human habit, hailing back as far as ancient Sumerians and Babylonians, but it is no less an arbitrary way to measure angles as would be any other. Why not split a full circle into 100 pieces? Or 1000? Well, the ancients thought there was 360 days in a year so they just split the celestial Sun circle in 360 pieces - one per day. It stuck.

With radians, the length of an arc segment becomes a simple product of the angle value and the radius. A full circle? 2*pi radians; a half-circle? just pi. A right angle? pi/2 - and so on.

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OK the lite finally came on. Essentially what a radian does is use the circumferance to derive the angle.
2 pi R = one radian
Ie for a 90 degree it would be 1/4 of 2 pi R (one rad) or pi/2 R.

R would be scientific notation (uhh symbol) for radius ??
What is scientific notation for radian?

OK someone cook me up 3 fairly simple problems utilizing radians as applied to a wheel eg a car tire.

Hmmm tire has diameter of 20" so one rad rotation = 2 pi 10 = 62.8 inches travel.

If tire is doing 100 RPM then it travels 2 pi 10 x 100 = 6280 inches in one minute.

Another lite comes on
NOW let us see
HP = 550 lbs one foot in one second
If I have a 2 foot diameter drum and load is 550 lb tehn
it will take 1 HP to lift load one foot
one foot travel is 1/6.28

OK so formula HP = (T x RPM)/5252 I know is derived from above and incorporating in radians and converting from minute to second.
HP = 550 lb one foot x one foot travel per second

HP = 550 ft lb / 6.28 X 60 second
= 33,000 /6.28
= 5254 x T x RPM

OK where am I going wrong?? This was explained to me in a post but I cannot find it
Dan Bentler

OK I found other post and think I know where I went wrong. Let me do some thinking before anyone wastes their time. I will post my new self taught knowledge. I sure wish I had a better instructor.

leitmotif said:

Uhhh value for slope - correct?
Dan

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400 gradians in a circle. Since when do physical constants have to be nice round numbers (pun intended)?

You can thank the same folks who decided that today should be the 8th day in a 9 day work week (ironic now that the same have a 35 hour week) with one day off, and the 17th day of the third month of the year 218. Thankfully that one never caught on.