[Blindmath] Important angles

[Nelson Blachman]

  A proper understanding of trigonometry requires knowing the 6 
trigonometric functions of the angles 0º, 30º, 45º, 60º, 90º, 120º, 135º, 
150º, 180º, ... as well as -30º, -45º, ....  These merely involve 1/3, 1/2, 
and 2/3 of a right angle, which shouldn't be too hard to imagine without 
pictures.

  Nelson, retired physicist
  Oakland, California
----- Original Message ----- 
From: "Salisbury, Justin Mark" <SALISBURYJ08 at students.ecu.edu>
To: "Blind Math list for those interested in mathematics" 
<blindmath at nfbnet.org>
Sent: Sunday, December 12, 2010 9:04 PM
Subject: Re: [Blindmath] Unit Circle


> Hi Jill,
>
>   That circular geoboard that I showed you can help with the quadrants and 
> many angles.  In order to find a product that will fit your daughter's 
> needs, you'll need to know which angles she'll need on the tool.  There 
> are infinitely many angles in every circle, and no fixed solid device is 
> going to hold all angle measurements.  Once she comes to understand the 
> concept of the basic trigonometric functions (such as sine, cosine, and 
> tangent) with a simple tactile device, such as the circular geoboard, she 
> should be able to calculate any angle measurement she needs.  The point of 
> this course is not to memorize too many angle measurements; your daughter 
> will be learning how to calculate angle measurements from coordinates and 
> coordinates from angle measurements.
>
>    If you wish to give her a table of some of the trig functions for some 
> of the most commonly used values, anyone fluent in Braille can transcribe 
> that for her from a visual table, which is guaranteed to exist in the 
> standard textbook if the students will need it.  Again, I think that the 
> function of these tactile models will really be to teach her the concept 
> of what she is doing and what it means.
>
> Good luck!
>
> Justin
>
>
>
> Justin M. Salisbury
> Undergraduate Student
> The University Honors Program
> East Carolina University
> salisburyj08 at students.ecu.edu
>
> "It is the mark of an educated mind to be able to entertain a thought 
> without accepting it."    -Aristotle
> ________________________________________
> From: blindmath-bounces at nfbnet.org [blindmath-bounces at nfbnet.org] on 
> behalf of Brad and Jill Weatherd [snowedin at union-tel.com]
> Sent: Sunday, December 12, 2010 8:44 PM
> To: 'Blind Math list for those interested in mathematics'
> Subject: Re: [Blindmath] Unit Circle
>
> Hi Justin and others,
> Thanks so much for responding so quickly!  She just needs either a 
> Brailled
> and raised line unit circle showing the 4 quadrants, the angles, the
> degrees, and radians or even a table that includes that information would 
> be
> great.  I'm thinking I could make some kind of a table, but I'm pretty
> math-impaired so that might not be such a good idea.  Got any ideas? 
> Thanks
> again, Jill
>
> -----Original Message-----
> From: blindmath-bounces at nfbnet.org [mailto:blindmath-bounces at nfbnet.org] 
> On
> Behalf Of Salisbury, Justin Mark
> Sent: Saturday, December 11, 2010 6:50 PM
> To: Blind Math list for those interested in mathematics
> Subject: Re: [Blindmath] Unit Circle
>
> Hi Joel,
>
>    I am a mathematics major and am very familiar with said unit circle.
> The equation x^2 + y^2 = 1 is the correct equation for it.  Are you 
> looking
> for an accessible version of one such as a raised-line drawing of a unit
> circle, or were you merely looking for the information on what the unit
> circle is?
>
> Good luck!
>
> Justin
>
> Justin M. Salisbury
> Undergraduate Student
> The University Honors Program
> East Carolina University
> salisburyj08 at students.ecu.edu
>
> "It is the mark of an educated mind to be able to entertain a thought
> without accepting it."    -Aristotle
> ________________________________________
> From: blindmath-bounces at nfbnet.org [blindmath-bounces at nfbnet.org] on 
> behalf
> of Sina Bahram [sbahram at nc.rr.com]
> Sent: Saturday, December 11, 2010 8:01 PM
> To: 'Nelson Blachman'; 'Blind Math list for those interested in 
> mathematics'
> Subject: Re: [Blindmath] Unit Circle
>
> This might help explain what he's looking for.
>
> http://www.mathsisfun.com/geometry/unit-circle.html
>
> Take care,
> Sina
>
> -----Original Message-----
> From: blindmath-bounces at nfbnet.org [mailto:blindmath-bounces at nfbnet.org] 
> On
> Behalf Of Nelson Blachman
> Sent: Saturday, December 11, 2010 7:06 PM
> To: Blind Math list for those interested in mathematics
> Subject: Re: [Blindmath] Unit Circle
>
>  The only unit circles I know are any circle whose radius is 1 or else the
> circle whose center is at the origin (0,0) and has equation
> x^2 + y^2 = 1.
>
>  Nelson
> ----- Original Message -----
> From: "Brad and Jill Weatherd" <snowedin at union-tel.com>
> To: <blindmath at nfbnet.org>
> Sent: Saturday, December 11, 2010 2:59 PM
> Subject: [Blindmath] Unit Circle
>
>
>> Hi Everyone,
>>
>> My daughter needs some accessible version of the Unit Circle for her
>> senior Trig/pre-calculus class.  Does anyone have any idea where we
>> can get our hands on something like this?  Even something in table
>> form might work.
>> Thanks so much for any help!  Jill Weatherd, Wyoming
>>
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>
>
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