Trigonometry Resource

Sferics · Post by **Sferics** » Sat Jul 26, 2008 3:09 pm

I am going to be taking Calculus BC at a local college this year, but since I have yet to learn trigonometry, they are offering a quick two week course this summer (which I am currently in). I realize the time limitations and that I will probably only be taught what is necessary for calculus.

I do know the basic trigonometric functions and how they look on a graph, and am pretty familiar with the unit circle. I am told even this would probably be sufficient to get me through calculus, but I also understand a strong background in trigonometry would help me not only in calculus, but also later on.

So with these time limitations in mind, I see that I will have to do some learning on my own to facilitate my want for a more complete understanding of the subject. So basically, what I am asking of you zboards is a recommendation for a supplementary trigonometry text for the next two weeks.

Many thanks.

Post by **grinvader** » Sat Jul 26, 2008 3:35 pm

I can't advise you texts (never been a bookworm) but here's what's to know about trig:

- basic definitions and applications (relation between triangle sides and angles)
- direct consequences of definitions
- modulo 2*pi and its consequences
- expressing cos in function of sin and various square/products combination formulas
- derivatives/primitives (clockwise to derivate, counterclockwise to integrate)
- exponential definitions and applications [need complex numbers]

whicker · Post by **whicker** » Sat Jul 26, 2008 10:13 pm

also, cordic is fun to look at, if you're into programming.

Sferics · Post by **Sferics** » Sat Jul 26, 2008 11:00 pm

grinvader wrote:I can't advise you texts (never been a bookworm) but here's what's to know about trig:

- basic definitions and applications (relation between triangle sides and angles)
- direct consequences of definitions
- modulo 2*pi and its consequences
- expressing cos in function of sin and various square/products combination formulas
- derivatives/primitives (clockwise to derivate, counterclockwise to integrate)
- exponential definitions and applications [need complex numbers]

I am not sure what you mean when you say consequences? Do you mean their applications?

I am guessing modulo 2*pi is for the revolutions of the unit circle?

As far as derivatives and integrals go, I was unaware that trigonometry covered that material... I have limited/no knowledge on those and was expecting to learn them during calculus.

Also, during my education thus far, I've always been told what the trigonometric ratios are (tan, sin, cos, ect) but never what they actually mean. I understand they are the same ratios tested, tried, and true, but this explanation has never felt adequate, if that makes any sense... Anyone know where I could read a thorough explanation of what they really are, why their graphs look like they do, ect ? I know I'll probably get some "just accept it for what it is" responses, and maybe that's all there is to it.

creaothceann · Post by **creaothceann** » Sat Jul 26, 2008 11:17 pm

Sferics wrote:... and was expecting to learn them during calculus.

Why wait? Wikipedia is your friend too.

Sferics · Post by **Sferics** » Sat Jul 26, 2008 11:51 pm

creaothceann wrote:
Sferics wrote:... and was expecting to learn them during calculus.
Why wait? Wikipedia is your friend too.

By learning them in Calculus, I meant that I will learn it in my own calculus text after I feel I have a strong grasp of trigonometry, which will probably be before we go over it in class and on my own anyway.

Anyway, I have already researched some of these things on Wikipedia, and I find it's not the best source to learn from.

DOLLS (J) [!] · Post by **DOLLS (J) [!]** » Sun Jul 27, 2008 1:51 am

Mathworld is your (better) friend.

The ratios are what they are, you need no more explanation than to visualize the longitude of the sides of the right triangle in relation to the hypotenuse as you sweep along the circle. There are clear geometric representations for many of the trigonometric functions. An identity table will come in handy.

If the cartesian representation of the circle is giving you headaches (x² + y² = r²), understand the parametrization of the circle as a function of theta and r, it may help you grasp things a little bit better.

Suggestions:
http://mathworld.wolfram.com/Trigonometry.html

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

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

Rashidi · Post by **Rashidi** » Sun Jul 27, 2008 2:19 am

derivates, integrals

i always sucks at these, luckly my teacher let me pass with minimal grade...

for me, anyway one interesting in trig is about Lissajous Curve, especialy since it perfectly draw-able using computer programming, yeah cordy is fun.
other fun is to figuring trig equations from a spirograph ... (and thus try to draw your own modified spirograph using programming language)

Sferics · Post by **Sferics** » Sun Jul 27, 2008 2:19 am

DOLLS wrote:Mathworld is your (better) friend.

The ratios are what they are, you need no more explanation than to visualize the longitude of the sides of the right triangle in relation to the hypotenuse as you sweep along the circle. There are clear geometric representations for many of the trigonometric functions. An identity table will come in handy.

If the cartesian representation of the circle is giving you headaches (x² + y² = r²), understand the parametrization of the circle as a function of theta and r, it may help you grasp things a little bit better.

Suggestions:
http://mathworld.wolfram.com/Trigonometry.html

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

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

About the functions, that's what I thought. Just seemed like back in middle school when I first saw them and what they could do, and now to learn they are simply ratios is kind of disappointing. I did however find a formula to find the trigonometric functions of any angle analytically, so maybe there is more to it than meets the eye.

I appreciate the links, I will check those out.

DOLLS (J) [!] · Post by **DOLLS (J) [!]** » Sun Jul 27, 2008 4:53 am

Sferics wrote:I did however find a formula to find the trigonometric functions of any angle analytically, so maybe there is more to it than meets the eye.

This is always the case in math.

Sferics · Post by **Sferics** » Sun Jul 27, 2008 7:04 am

I have seem to run into a problem I can't solve. Maybe someone here can help me out.

http://i95.photobucket.com/albums/l124/ ... 1217137938

Both these circles are revolving in the same direction. It takes the larger circle 23.933 hours to revolve and the smaller circle 2.231 hours to revolve. Notice the points on each circle. How long will it be before the two points re-align?

So far, I know the angular speeds of the circles, (2*pi)/23.933 and (2*pi)/2.231, and that I need to set up an equation, but I am stuck... help?

creaothceann · Post by **creaothceann** » Sun Jul 27, 2008 9:24 am

Hint:

Code: Select all

t * v.L = p.L
t * v.S = p.S

p.L modulo 360° = p.S modulo 360°

t = time, v = velocity of the larger/smaller circle, p = position

The position p given by each equation is not normalized, i.e. it may be larger than 360°. You can use the sinus or cosinus function for that.

Sferics · Post by **Sferics** » Sun Jul 27, 2008 6:07 pm

creaothceann wrote:Hint:
Code: Select all
t * v.L = p.L
t * v.S = p.S

p.L modulo 360° = p.S modulo 360°
t = time, v = velocity of the larger/smaller circle, p = position

The position p given by each equation is not normalized, i.e. it may be larger than 360°. You can use the sinus or cosinus function for that.

How would I solve for the modulo? I know what it means, but I've never known how to actually solve them...

Sferics · Post by **Sferics** » Sun Jul 27, 2008 6:59 pm

My TI-89 saves the day with mod() and solve(). The solution I have reached is that they will re-align every 140.968 hours. This was however one of those "project, take it home and screw around with it" problems in my PreCalculus book, and it does not have a solution for this problem in it. Can anyone verify my answer?

Also, would it be feasible to solve this problem analytically? and how?

Post by **odditude** » Sun Jul 27, 2008 8:04 pm

Sferics wrote:How would I solve for the modulo? I know what it means, but I've never known how to actually solve them...

mod is the remainder after long division, 4th-grade style (before you knew decimal division).

Sferics · Post by **Sferics** » Sun Jul 27, 2008 8:17 pm

odditude wrote:
Sferics wrote:How would I solve for the modulo? I know what it means, but I've never known how to actually solve them...
mod is the remainder after long division, 4th-grade style (before you knew decimal division).

I understand this, but it gets kind of hard to solve for when they are the same and with the values above.