# Foo - How do you figure sine, cosine, and tangent, with out a calculator?

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ChAnMaN
12-08-04, 09:58 PM
ok so today in math we are working with sine, cosine, and tangent long story short i asked the teacher how to figure it out with out the use of a calculator and his response was the "you dont" in a way like he was telling me i wouldnt be able to understand. this made me really mad so i looked online but i couldnt find it on the internet either so i was hoping maybe some math wiz here would be able to tell me the answer.

thanks
ChAnMaN

slvoid
12-08-04, 10:01 PM
Sohcahtoa.
Sin=Opposite/Hypotenuse.

ChAnMaN
12-08-04, 10:05 PM
no not like that i understand soh cah toa i mean acutlay calculate it like cos34=? normaly on your calculator you push "cos" , push 34, hit enter and it spits out a number i want to know the equation that goes into that

trekkie820
12-08-04, 10:09 PM
Do you own a calculator that will do it?

If you are in high school, a word of advice. After your college courses in these areas, trig is USELESS.

CdCf
12-08-04, 10:10 PM
http://www.homeschoolmath.net/other_topics/sine_calculator.php

JavaMan
12-08-04, 10:20 PM
You can calculate it (not advised) or you can look it up in a table. Before calculators, we used trig tables. http://www.math2.org/math/trig/tables.htm

It's very simple to use a table like this, but you have to interpolate if you want a value in between the table listings.

Tom

CRUM
12-08-04, 10:21 PM
http://www.homeschoolmath.net/other_topics/sine_calculator.php

Cool Site. Thanks.

bikeNaround
12-08-04, 10:23 PM
If you are in high school, a word of advice. After your college courses in these areas, trig is USELESS.
Not true for many professions. Maybe useless to you but not to everyone.

CdCf
12-08-04, 10:26 PM
Pretty easy to set up in Excel as well.
It took me about a minute.

CRUM
12-08-04, 10:26 PM
Just because we choose not to use knowledge, doesn't make it useless. I think it is great you are trying to know more than "punch this button and this will happen". Keep that curious nature. It will only help you down the road.

Swiss Hoser
12-08-04, 10:28 PM
The link to "homeschoolmath" identifies it as a Taylor series. It's actually a special case of this called the Maclaurin series.

ChAnMaN
12-08-04, 10:50 PM
hey thanks for the homeschoolmath link, im playing with it right now to see if i understand the equation completely

blendingnoise
12-09-04, 03:45 AM
If it is certian angles or combinations of known angles (45, 30) you can figure out a solution using a law whose name I forget. It goes something like sin(75) = sin45 + sin30 and then using the basic 45/45/90 and the 60/30/90 triangles you can get a solution. It has been a year since I did trig but I do remember that part.
Back when I was in India we had to look up logs in these log table books which was not fun during exams and such. Good for basics and understanding but a calculator is much more helpful for calculations like those.

12-09-04, 05:44 AM
I never understood that stuff.
My math teachers never related it to real life, all I understood was that I was trying to find the length of line A-B. Why would anyone care?
Now, I realize that I could have found the height of a tree or house. Well, ok, I wasn't too bright, no brilliant leaps of logic here.

slvoid
12-09-04, 06:05 AM
You can probably do this with algebra. It's all just a ratio, so knowing that a given angle in a right-triangle can go from just above 0 to just below 90 degrees, you can setup a ratio of the sides then subdivide that through the 0-90 degrees, the smaller your subdivision, the more precise your answer.

MERTON
12-09-04, 08:54 AM
Do you own a calculator that will do it?

If you are in high school, a word of advice. After your college courses in these areas, trig is USELESS.

trig is not useless!

MERTON
12-09-04, 08:56 AM
for the angle use

tan^-1 (ho/ha)
sin^-1 (ho/h)
cos^-1 (ha/h)

MERTON
12-09-04, 08:57 AM
You can calculate it (not advised) or you can look it up in a table. Before calculators, we used trig tables. http://www.math2.org/math/trig/tables.htm

It's very simple to use a table like this, but you have to interpolate if you want a value in between the table listings.

Tom

i heard it took like 5 days to do problems like that. :eek:

H23
12-09-04, 09:08 AM
Here is a nice list of expansions for common trig functions....

http://mathworld.wolfram.com/MaclaurinSeries.html

A nice thing about expansions is that you can often approximate a numerical computation by expanding the special functions (trig functions) and using only the first couple of terms (if you know subsequent terms are vanishingly small).

In the before time, that's what people did to make some calculations tractable.

iamlucky13
12-10-04, 12:48 AM
"Trig is USELESS" Hehe...not quite. Some of the stuff you use it for are a little mundane, like designing the chair you are sitting on, but some are kind of cool, like solving differential equations that describe the wave motion of light, an understanding that led to the invention of lasers and CD players.

PanPanX
12-10-04, 09:35 AM
you learn something called the unit circle. 99.9% of the time when you do trig problems, and you're not allowed to use a calculator, they're 'special' ones that have values like pi/4, pi/3, pi/6, pi/2, 1, 0, 3pi/2, etc etc etc. just learn the unit circle, and know a tiny bit of algebra and you can solve all the 'special ones'. and what i mean by that, is you can solve for the sin, cos, tan, csc, sec, cot, arcsin, arccos, arctan, arccsc, arcsec, arccot of 0, 30, 60, 90, 120, 150, 180, 210, 240, 270, 300, 330, 360, 45, 135 degrees

and for everything else, you have to use some equations and whatnot. some trig identies, and properties, and you'll be set. a common trig idenity is (sinX)^2 + (cosX)^2 = 1

you'll be learning a lot of this when you take PreCalc and Calc. :D

and whoever said Trig is useless after college corses and stuff is completely wrong. electrians use the cos curve everyday to calculate the power and watts and such that you need. circuts, your house, everything, is all calculated by either using sin or cos curves. of course if you're flipping burgers, its completely useless.. unless you're really sick and demented and lke to flip your burgers at a certain trig curve or like to compare the steam different trig curves..

hehe also, you know the button on your calculator that changes it from DEG, RAD and (something else i cant think of off the top of my head). the Degree stands for Degrees and Rad stands for Radians, and the other thing is used for Mech Engineers to calculate certain things.. but later on you'll learn to solve trig stuff in degrees and in radians mode. right now you're probably just using degrees

H23
12-10-04, 10:28 AM
I think the guy that was saying trig was useless after college courses, was trying to say that there is so much more to math that at some point all the things you learned in high school math are nothing more than tiny fragments of the big picture in math.

To the kiddies out there... stick with it if you have an inclination for math, there is a lot more to it, and it does get vastly more interesting.

iamlucky13
12-10-04, 03:06 PM
...and it does get vastly more interesting.

Right up until you get to partial differential equations and get stuck with a teacher who doesn't seem to realize his method is less like teaching you how to solve PDE's than it is discussing different methods with you as though you were his acedemic peer. I just need to repeat to myself "I will pass the final, I will pass the final..." and spend all of the next 5 days studying. It's a pity because I was really excited about taking this class at the beginning of the semester.

PanPanX
12-10-04, 03:33 PM
Right up until you get to partial differential equations and get stuck with a teacher who doesn't seem to realize his method is less like teaching you how to solve PDE's than it is discussing different methods with you as though you were his acedemic peer. I just need to repeat to myself "I will pass the final, I will pass the final..." and spend all of the next 5 days studying. It's a pity because I was really excited about taking this class at the beginning of the semester.

yea.. i was like that.. i used to think math was cool and fun and interseting.. but then i had a crappy teacher and now i dont even know if im going to pass.. :(

LordOpie
12-10-04, 06:11 PM
Do you own a calculator that will do it?

If you are in high school, a word of advice. After your college courses in these areas, trig is USELESS.
:rolleyes:

GeezerGeek
12-10-04, 08:50 PM
I used a slide rule to find trig functions when I was in school.

Swiss Hoser
12-14-04, 12:42 PM
I used a slide rule to find trig functions when I was in school.
So did I.
Man, am I glad those days are gone!