Can someone help me with Algebra II?

[Firestar]

So, basically, for large chapters we have a large assignment. And, like the idiot I am, I procrastinated one of the things (the assignment is essentially a compilation of smaller assignments) that is probably the biggest assignment, and now, I'm essentially completely lost.

I'll start off with the very first problem:

Suppose you are at the center of a circle with a radius of 1 mile. How far left or right and how far up or down must you move in order to end up on the boundary of the circle, with a final angle of 22 degrees with respect to the horizontal axis?

There are other problems based on this one, but I think if I understood how to answer this one, I could answer the others on my own.

So, my confusion with this problem is that, well, I have no idea how to do this. I understand that we have to move a certain amount to the right and up, but I'm not sure of how much. Our teacher didn't ever teach us anything relevant to this, so I have no idea why it's on this, but currently that's not of much importance. The most relevant formula to this that I've ever been tought in Algebra II is that s=rθ (s=the length of the circle's boundary, r=radius, θ=degree in radians), but I'm not really seeing how that would help me.

Nevermind, I got this one. I figured it out using a program she linked us to (I would put a link here but it has my teacher's name on it).

The second problem I'm having trouble with is this:

In general, does Earth have a constant period in its orbit around the sun? If so, what is the period? If not, explain why not.

My problem with this problem is that, well, the Earth's orbit is not a cos/sin/tan graph. It's a circle/elipsis.

This problem also has other problems built off of it, but the same applies as before.

Please help me through my idiocy.

 

[wywern209]

the earth does. it is 365 days? the first problem can be solved with sohcahtoa.

 

[JoltinJoe]

Think of cosine being associated an x value and the sine of the angle being associated with the y value. You can see this quickly where the unit circle intersects the x and y axes. At point (cos(0), sin(0)) corresponds with (1,0). (cos(90), sin(90)) corresponding with (0,1), etc.

By this logic, (cos(22), sin(22)) is a point at (.9272, .3746).



You are right that the sine wave is periodic, but it is not the only thing that is. The earth's rotation around the sun is definitely periodic, completing one revolution in 365.242 (the fraction is more than two places) days. This is why we have leap days (to account for the lost day) every four years (except for years that are divisible by 100 (2012, 2008, 2004, 2000) and except for years that are also divisible by 400 (2000, 1600 were leap years, but not 1700, 1800, 1900).

 

[dukebound85]

So, basically, for large chapters we have a large assignment. And, like the idiot I am, I procrastinated one of the things (the assignment is essentially a compilation of smaller assignments) that is probably the biggest assignment, and now, I'm essentially completely lost.

I'll start off with the very first problem:



There are other problems based on this one, but I think if I understood how to answer this one, I could answer the others on my own.

So, my confusion with this problem is that, well, I have no idea how to do this. I understand that we have to move a certain amount to the right and up, but I'm not sure of how much. Our teacher didn't ever teach us anything relevant to this, so I have no idea why it's on this, but currently that's not of much importance. The most relevant formula to this that I've ever been tought in Algebra II is that s=rθ (s=the length of the circle's boundary, r=radius, θ=degree in radians), but I'm not really seeing how that would help me.

Nevermind, I got this one. I figured it out using a program she linked us to (I would put a link here but it has my teacher's name on it).

The second problem I'm having trouble with is this:



My problem with this problem is that, well, the Earth's orbit is not a cos/sin/tan graph. It's a circle/elipsis.

This problem also has other problems built off of it, but the same applies as before.

Please help me through my idiocy.

1) x = cos(22)
y = sin 22

2) yes......for the purposes of that class. i would imagine The period is 1 year (time takes to do one rev)

though it does change ever so slightly

 

[fireshot91]

I don't think they learn sin/cos/tan in Algebra II?

I think the first time I heard it was in Geometry, and while I did Algebra I>Geometry>Algebra II, half of my school did Geometry after Algebra II.

 

[blesscheese]

Hey,
It sounds like you answered your first question on your own...

Regarding your second question, not to be a pain, but does your textbook have a definition of what a period is? After reading that definition, do you think the earth's orbit around the sun would meet that definition, or not?

Feel free to post any more questions....

 

[Firestar]

Think of cosine being associated an x value and the sine of the angle being associated with the y value. You can see this quickly where the unit circle intersects the x and y axes. At point (cos(0), sin(0)) corresponds with (1,0). (cos(90), sin(90)) corresponding with (0,1), etc.

By this logic, (cos(22), sin(22)) is a point at (.9272, .3746).

That's what I got, thanks!

You are right that the sine wave is periodic, but it is not the only thing that is. The earth's rotation around the sun is definitely periodic, completing one revolution in 365.242 (the fraction is more than two places) days. This is why we have leap days (to account for the lost day) every four years (except for years that are divisible by 100 (2012, 2008, 2004, 2000) and except for years that are also divisible by 400 (2000, 1600 were leap years, but not 1700, 1800, 1900).

Oooh, I see, thanks. I didn't think about the year being the period.

the earth does. it is 365 days? the first problem can be solved with sohcahtoa.

I got the first problem earlier, I barely remember anything from geometry though, thanks.

1) x = cos(22)
y = sin 22

2) yes......for the purposes of that class. i would imagine The period is 1 year (time takes to do one rev)

though it does change ever so slightly

Thanks.

I don't think they learn sin/cos/tan in Algebra II?

You learn their relation to the unit circle. You learn their relation to trangles in Geometry.

I think the first time I heard it was in Geometry, and while I did Algebra I>Geometry>Algebra II, half of my school did Geometry after Algebra II.

I'm doing it the same way you did, but we didn't learn about graphing and their relation to unit circles in Geo.

Hey,
It sounds like you answered your first question on your own...

Yeah, I figured it out after playing with a webpage and a few formulas.

Regarding your second question, not to be a pain, but does your textbook have a definition of what a period is? After reading that definition, do you think the earth's orbit around the sun would meet that definition, or not?

You're not a pain at all! I appreciate the help a lot. I'm not really sure of how the book defines it, but the notes I have says it's "the length of one cycle".

 

[blesscheese]

OK, looking up period in my MacBook Air's dictionary, I get:
• Physics the interval of time between successive occurrences of the same state in an oscillatory or cyclic phenomenon, such as a mechanical vibration, an alternating current, a variable star, or an electromagnetic wave.
• Astronomy the time taken by a celestial object to rotate around its axis, or to make one circuit of its orbit.
• Mathematics the interval between successive equal values of a periodic function.

By these definitions, I would say that the earth's orbit is a periodic function. I was asking what your book's definition was, because that is typically the way a mathematician thinks. Don't worry, I don't think I read any of my high school books at all; I think it was only at college that I learned that I needed to.

Can you think of any other things that would meet the definition of a period, and a periodic function? What about a clock? A calendar?

 

[acidfast7]

At noon Terrestrial Time (TT) on J2000.0 a single orbit took 365.256363004 days.

That should be all you need to know.

 

[eric/]

Khan academy

 

[Firestar]

Can you think of any other things that would meet the definition of a period, and a periodic function? What about a clock? A calendar?

Would they? I guess those apply.

Thanks everyone. I turned it in today, it should be fine.

 

[iJohnHenry]

Can you think of any other things that would meet the definition of a period, and a periodic function? What about a clock? A calendar?

Birth-control pills?

 

[blesscheese]

Would they? I guess those apply.

Thanks everyone. I turned it in today, it should be fine.

I'm not sure which way your class will go with the algebra, trig, and period ideas. One direction would be frequency and waves (the more trigonometry direction). The other direction would be more algebraic, or number theory even, and start discussing modular arithmetic ideas.

I'm guessing the first, and not the latter, but I could be wrong. I hope it went well!