need help on sine wave

[akcapr]

i need to answer some of these problems, and i do not know wat a sine or cosine wave is. I need help with numbers 11, 13 and 15. I would greatly appreciate any help.

[akcapr]

is anyone willinh to help?!?!?! please?

[jordan]

You might need to add a little more of the previous problems first. It looks like this one picks up at the end of it and I don't exactly know what is going on with the pedals.

[akcapr]

wel lthe circumference of thwe wheel is 232.478 cm, that should be all you need to solve it. Im still trying to figure out what number 11 is. this picture may help understand it.

[jordan]

Ok, the picture helps.

 

According to the picture, the height of the pedal will vary between 100mm and 440mm depending on where it is. It can never excede these values and will hit every value in between. Therefore, sine and cosine are helpful because they range from 0 to 1 with every value in between but none outside. The sine curve, for example, starts at 0 for 0 degrees and then increases to 1 at 90 degrees and then beck to 0 for 180 degrees and so on for whatever values of x degrees you can want. The pedal starts at 100mm and goes up to 440mm and then back to 100mm and so on. Therefore, the sine curve (or cosine) can be manipulated to give the height of the pedal so that it remains within the bounds that the picture shows the pedal needs to remain in.

[uncool]

Jordan, remember, sine and cosine go from -1 to 1.

And a sine can be made into a cosine, with a shift of 90 degrees. Therefore, if you can use one, you can use the other.

As for the formula:

y = amplitude (170) * sine (or cosine) (2*pi*frequency*t+someshift) + average

-Uncool-

[jordan]

Oh yeah, stupid mistake. Don't know why I put 0 instead of -1. Sorry about that.

[akcapr]

why can i use sin and cos but not tangent?

[akcapr]

and also, how would i solve #15?

[jordan]

Tangent isn't a continuous function.

 

Is there a circumfrence or diameter for the other two wheels? And which one is the "right" pedal and which is the "left"?

 

Your basic method is going to be to see how many revolutions (or what fraction of a revolution) the big wheel is going to have to make to move 1m. Then translate that into revolutions for the small wheel with the pedals. Find where that puts the desired pedal and then use trig ratios to find how far off the ground it is. I'm not sure there is enough information given in the problem to solve that right now.

[dryga]

why can i use sin and cos but not tangent?

because sine and cosine can be considered to be the same function, since they are related by [math]\sin x = \cos (x + \frac{\pi}{2})[/math]. Tangent, OTOH, is defined by [math] \tan x = \frac{\sin x}{\cos x} [/math], so it looks very different from both sine and cosine.

 

Plots of sine, cosine and tangent can be found here (note the similarity between sine and cosine):

 

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

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

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