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Old 30-03-2015, 08:31   #16
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Re: Trigonometry question...

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Originally Posted by OldFrog75 View Post
What goes inside the parentheses for PI()? Didn't quite understand that.
Nothing go in the parentheses. The () tells excel that PI() is a function and to evaluate it. Excel then evaluates it by replacing PI() with the mathematical value of pi (3.1415926...) to very high precision. It is just a querk in Excel's programming language.

Doug
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Old 30-03-2015, 14:06   #17
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Re: Trigonometry question...

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Originally Posted by Seaworthy Lass View Post
Nothing, if you enter PI() then the value for pi is inserted.
I'm using Excel spreadsheet and not getting the right answers. Might be using wrong formulas for example:

=COS(30)
=1/COS(30)
=1/(COS(2*PI()/30))

None of these formulas give me the expected result:

A = 0.15; not 0.866
B = 6.48; not 1.15
C = 1.02; not 1.15

It appears I have to convert to radians or something.
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Old 30-03-2015, 14:15   #18
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Re: Trigonometry question...

Simplest way to handle the degrees to radians in Excel:

=1/COS(RADIANS(30))
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Old 30-03-2015, 14:19   #19
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Re: Trigonometry question...

Quote:
Originally Posted by OldFrog75 View Post
I'm using Excel spreadsheet and not getting the right answers. Might be using wrong formulas for example:

=COS(30)
=1/COS(30)
=1/(COS(2*PI()/30))

None of these formulas give me the expected result:

A = 0.15; not 0.866
B = 6.48; not 1.15
C = 1.02; not 1.15

It appears I have to convert to radians or something.
The formula given by Dougdaniel is incorrect.
This is the correct one.

L8 is the distance in a straight line:

Quote:
Originally Posted by Seaworthy Lass View Post
... the distance travelled tacking =L8/(COS(2*PI()*L7/360))
Where L7 is the angle off the true wind in degrees.

OldFrog, if you are using a calculator, it may have a cos button. Just check 'deg' is written in tiny writing in the corner of the screen (if not, press the deg/rad button), enter the angle off the true wind and hit 'cos'.

All you need to do is divide the actual straight line distance by this figure and you have the distance travelled tacking .

SWL
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Old 30-03-2015, 14:34   #20
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Re: Trigonometry question...

Quote:
Originally Posted by Seaworthy Lass View Post
The formula given by Dougdaniel is incorrect.
This is the correct one.

L8 is the distance in a straight line:

Thanks. That works.

But why doesn't "=COS(30)" or "1/COS(30)"?


Never mind. I figured it out. Should be:

"=COS(Radians(30))" or "1/COS(Radians(30))"
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Old 30-03-2015, 14:37   #21
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Re: Trigonometry question...

Quote:
Originally Posted by OldFrog75 View Post
I'm using Excel spreadsheet and not getting the right answers. Might be using wrong formulas for example:

=COS(30)
=1/COS(30)
=1/(COS(2*PI()/30))

None of these formulas give me the expected result:

A = 0.15; not 0.86
B = 6.48; not 1.15
C = 1.02; not 1.15
I have prepared an excel spreadsheet for you and uploaded it.
In it, you enter the straight line distance in B1. This will be the long side of your isosceles triangle.
Enter the angle off the wind in degrees in B2.
I convert degrees to radians for you. The answer will appear in B3.
Then the distance over the bottom appears in B4.

Your third formula is almost right.

If you had tried:
Distance over bottom = straight line distance / (COS(2*PI()*)Angle off wind/360)), you would have had it.

To convert from degrees to radians, divide the angle in degrees by 360 and multiply by the result by twice pi.
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Old 30-03-2015, 14:41   #22
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Re: Trigonometry question...

Quote:
Originally Posted by StuM View Post
Simplest way to handle the degrees to radians in Excel:

=1/COS(RADIANS(30))
I just pulled the old netbook out to have a play .

Neat shortcut .
Rather than dividing into 1 though, the top figure need to be the straight line distance.

SWL
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Old 30-03-2015, 14:42   #23
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Re: Trigonometry question...

Quote:
Originally Posted by dougdaniel View Post
I have prepared an excel spreadsheet for you and uploaded it.
In it, you enter the straight line distance in B1. This will be the long side of your isosceles triangle.
Enter the angle off the wind in degrees in B2.
I convert degrees to radians for you. The answer will appear in B3.
Then the distance over the bottom appears in B4.

Your third formula is almost right.

If you had tried:
Distance over bottom = straight line distance / (COS(2*PI()*)Angle off wind/360)), you would have had it.

To convert from degrees to radians, divide the angle in degrees by 360 and multiply by the result by twice pi.
I didn't know about the RADIANS operator. That's the easiest way. Doug
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Old 30-03-2015, 14:43   #24
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Re: Trigonometry question...

Quote:
Originally Posted by OldFrog75 View Post
Thanks. That works.

But why doesn't "=COS(30)" or "1/COS(30)"?
Because Excel trig functions work on radians, not degrees. One radian is approximately 57 degrees. So Cos(30) calculates the cosine of 30 radians which is approximately 1719 degrees.
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Old 30-03-2015, 14:47   #25
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Re: Trigonometry question...

Quote:
Originally Posted by dougdaniel View Post

If you had tried:
Distance over bottom = straight line distance / (COS(2*PI()*)Angle off wind/360)), you would have had it.
Nearly right.
You need to leave out the bracket I have underlined

See the formula I gave above (or Stu's neat shortcut).

SWL
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Old 30-03-2015, 15:02   #26
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Re: Trigonometry question...

Hi SWL,

Perhaps you can explain why my formula works for me but not you? Did you try the attached spreadsheet?
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Old 30-03-2015, 15:10   #27
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Re: Trigonometry question...

Quote:
Originally Posted by dougdaniel View Post
Hi SWL,

Perhaps you can explain why my formula works for me but not you? Did you try the attached spreadsheet?
I could not see an attached spreadsheet.

Doug, the extra bracket before the word Angle is incorrect.
I have just plugged this in and I get an error message.

Use:
Distance over bottom
= straight line distance/(COS(2*PI()*Angle off wind/360))

NOT
Distance over bottom
= straight line distance / (COS(2*PI()*)Angle off wind/360))

I am sure you have just popped that extra bracket there in error
Please check again.

SWL
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Old 30-03-2015, 15:11   #28
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Re: Trigonometry question...

Quote:
Originally Posted by StuM View Post
Because Excel trig functions work on radians, not degrees. One radian is approximately 57 degrees. So Cos(30) calculates the cosine of 30 radians which is approximately 1719 degrees.

Yeah I finally figured that out. Got my spreadsheet together. Thanks everybody for all your help.

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Old 30-03-2015, 15:14   #29
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Re: Trigonometry question...

Quote:
Originally Posted by dougdaniel View Post
I have prepared an excel spreadsheet for you and uploaded it.
In it, you enter the straight line distance in B1. This will be the long side of your isosceles triangle.
Enter the angle off the wind in degrees in B2.
I convert degrees to radians for you. The answer will appear in B3.
Then the distance over the bottom appears in B4.

Your third formula is almost right.

If you had tried:
Distance over bottom = straight line distance / (COS(2*PI()*)Angle off wind/360)), you would have had it.

To convert from degrees to radians, divide the angle in degrees by 360 and multiply by the result by twice pi.
Never got the spreadsheet or can't find it. Thanks for the effort but I finally got the formulas straight and was able to build the spreadsheet I wanted.

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Old 30-03-2015, 16:15   #30
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Re: Trigonometry question...

That's only when the WPTs are close by. For distant WPTs you will be using spherical geometry and cos of the angle will not apply. See orthodrome distance and spherical triangle formulas.

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