Trigonometry question...

[dougdaniel]

Originally Posted by OldFrog75

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

[OldFrog75]

Originally Posted by Seaworthy Lass

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.

[StuM]

Simplest way to handle the degrees to radians in Excel:

=1/COS(RADIANS(30))

[Seaworthy Lass]

Originally Posted by OldFrog75

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:

Originally Posted by Seaworthy Lass

... 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

[OldFrog75]

Originally Posted by Seaworthy Lass

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))"

[dougdaniel]

Originally Posted by OldFrog75

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.

[Seaworthy Lass]

Originally Posted by StuM

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

[dougdaniel]

Originally Posted by dougdaniel

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

[StuM]

Originally Posted by OldFrog75

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.

[Seaworthy Lass]

Originally Posted by dougdaniel

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

[dougdaniel]

Hi SWL,

Perhaps you can explain why my formula works for me but not you? Did you try the attached spreadsheet?

[Seaworthy Lass]

Originally Posted by dougdaniel

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

[OldFrog75]

Originally Posted by StuM

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.

[OldFrog75]

Originally Posted by dougdaniel

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.

[barnakiel]

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.

b