ARCTAN Equation distilled

camerart · April 9th, 2018, 06:10 AM

Hi,
I've been given an equation for use in a project.
The system has limitations, e,g, it doesn't support '^'

Here is the equation: arctn= x/y/( 1+0.28125*( x/y )^2)*180/pi

Firstly does it look ok as an approximation of ARCTAN?

Second, is it possible to remove all brackets to show me the sequence of events, please?

Camerart

skipjack · April 9th, 2018, 07:39 AM

What is the argument of arctan?

camerart · April 9th, 2018, 09:40 AM

Quote:

Originally Posted by skipjack $View Post$

What is the argument of arctan?

Hi S,
If I understand correctly, x and y are READings from a computer module App 1 to 500.
C.

skipjack · April 9th, 2018, 05:54 PM

If x/y = 1, what value should the arctan have and what does the formula give? Now try another value for x/y, such as 0.5.

camerart · April 10th, 2018, 01:37 AM

Quote:

Originally Posted by skipjack $View Post$

If x/y = 1, what value should the arctan have and what does the formula give? Now try another value for x/y, such as 0.5.

Hi S,
Someone on a programming forum, has done this for me as I'm a bit of a dunce when it comes to maths and trigonometry, but to add to my confusion, I think he reversed X and Y.

I actually only want to see the equation distilled to without brackets, if possible, so I can work out how it works.

C.

skipjack · April 10th, 2018, 07:56 AM

arctan(u) = u/(1 + 0.28125u²) is a reasonable approximation for |u| < 1.
So is arctan(u) = u/(1 + 0.282u²).
The above both give a result in radians, so multiplying by 180$^\circ$/pi gives the value in degrees.

camerart · April 10th, 2018, 10:13 AM

Quote:

Originally Posted by skipjack $View Post$

arctan(u) = u/(1 + 0.28125u²) is a reasonable approximation for |u| < 1.
So is arctan(u) = u/(1 + 0.282u²).
The above both give a result in radians, so multiplying by 180$^\circ$/pi gives the value in degrees.

Hi S,
The original equation is working, but I'll try your neater version tomorrow, thanks.
C.

April 9th, 2018, 06:10 AM	#1
camerart Member Joined: Jan 2016 From: Uk Posts: 80 Thanks: 2	ARCTAN Equation distilled Hi, I've been given an equation for use in a project. The system has limitations, e,g, it doesn't support '^' Here is the equation: arctn= x/y/( 1+0.28125( x/y )^2)180/pi Firstly does it look ok as an approximation of ARCTAN? Second, is it possible to remove all brackets to show me the sequence of events, please? Camerart Last edited by skipjack; April 9th, 2018 at 07:38 AM.
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April 9th, 2018, 07:39 AM	#2
skipjack Global Moderator Joined: Dec 2006 Posts: 19,865 Thanks: 1833	What is the argument of arctan?
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April 9th, 2018, 05:54 PM	#4
skipjack Global Moderator Joined: Dec 2006 Posts: 19,865 Thanks: 1833	If x/y = 1, what value should the arctan have and what does the formula give? Now try another value for x/y, such as 0.5.
$skipjack is offline$

April 10th, 2018, 07:56 AM	#6
skipjack Global Moderator Joined: Dec 2006 Posts: 19,865 Thanks: 1833	arctan(u) = u/(1 + 0.28125u²) is a reasonable approximation for \|u\| < 1. So is arctan(u) = u/(1 + 0.282u²). The above both give a result in radians, so multiplying by 180$^\circ$/pi gives the value in degrees.
$skipjack is offline$

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