Sections 1 and 2
Oct 25th, 2010 by corricelli
Welcome!
Let’s use this location to post questions/concerns/information related to Honors Precalculus, Chapter 4, Sections 1 and 2!
Sincerely,
Mrs. Corricelli
44 Responses to “Sections 1 and 2”
Leave a Reply
Categories
- Algebra II (57)
- AP Comp Sci (3)
- Geometry (47)
- Math Talk (15)
- Motivational (6)
- Updates (91)
Get updates immediately!
Completely spam free, opt out any time.
Recent Comments
- corricelli on 11.1 – 11.3: Polygon Basics
- Sean W. on Geometry Videos & Links
- Katie Berry on 11.1 – 11.3: Polygon Basics
- Patrick on Earth is not a Sphere. What?!
- Patrick on 9.5 – Trig Ratios
So I just did the homework for 4.1 and I had some revelations. I wasn’t in class for the majority of Monday so I could be repeating what Mrs. Corricelli taught but I wanted to help anyone if I could. So I realized that to find two coterminal angles you have subtract the radian you have from 2π and for the second angle you have to add 2π
(or 360 if your using degrees) so that the angle is the same it just goes around once before reaching that point. Also it helped realizing that if you found the angle π/3 for example that the angle -2π/3 would connect to it, forming a line because the two must add up to equal 180 degrees and π/3 is equal to 60 degrees and -2π/3 is equal to -120 degrees, so if you go 60 degrees counter clockwise from the initial side and 120 clockwise from it you have traveled a total of 180 degrees and the two new terminal sides form a line. Again this may have been taught I really don’t know but figuring it out made it a lot quicker and I hope it helps someone. : ) oh and this π is the thing my computer uses for pi if it appears funny looking on some peoples computers.
Sam,
You are right on!!! Good for you!
Mrs. Corricelli
On the homework given out on 11/3 (the one about irrigation poles), concerning part B), what is it asking for when it says “find S and A”?
For the Wiki scorecard, I am a little confused. For one of the contributions, “You answered the question or solved the problem,” what if people had already answered the problem?
I already found an alternate solution to the problem, so how would I satisy the contribution stated above if the class already did it?
on the homework worksheet for tonight i dont understand what part b its asking you to find.
the question asks if o=135deg find S and A exactly
what are S and A?
I second Meg’s question…someone please answer!!
s = arc length.
A = area of the sector.
These are defined on the page.
Jeff,
Q: “what if people had already answered the problem?”
A: Then you cannot claim those points. You have to get to 10, whatever way you can.
Q: “I already found an alternate solution to the problem, so how would I satisfy the contribution stated above if the class already did it?”
A: I do not understand your question. Did you post about this? Then, claim it. If not, then pose another question or then find another way.
i am a little confused on how to do linear and angular speeds. for the homework for tonight, on page 290, how do you do #111?
yooo can someone post the hw for tonight?
can’t find my agenda. thanks!
rach the homework is p. 290 #s 91, 95-101 odd, 105 109 111 115 117 127
and can someone help me with number 105? I thought that by subtracting one latitude from the other id be able to find the degree in radians of the central angle, but im just really lost.
thank you becca!
hey Becca,
I think to answer that problem you need to look at where each city is located on the arc and then figure out their distance between them.
so you’re given a circle (because the two cities are on the same longitude) with a radius of 4000 mi you should be able to either subtract the angles then find the arc length, or find the arc length for both then subtract them and that should give you your answer.
yupp I’ll let you know when I’ve done it becca. But, for 97, how do you plot 2 diff lines on the stat plot thing?
Ok for 105,
I think you’re trying to find the arc length, because i see it in terms of a circle so they are both on the circle (that’s how i see it).
so if youre trying to find the arc length, the formula is S=rθ
The radius is 4000 miles.
But to find the central angle, you have to subtract one latitude from the other latitude (which you did).
41 15′ 50″ – 32 47′ 39″
but you cant have this because you cant subtract a larger number from a smaller number, so it becomes:
42 75′ 50″ – 32 47′ 39″= 8 28′ 11″
(if you don’t understand how to do that (because i didnt when i first did this problem), i can explain it in another post).
Change the 8 28′ 11″ into degrees by making the minutes and seconds into decimals (8+28/60+11/3600 (because you have to get a common denominator with the same units)
and you get 8.4697 degrees.
Then change that into radians, which makes it 0.1478 radians.
And then plug it into the S=rθ equation and you should get 591.2 miles.
Wow, that was REALLY long, sorry about that..if you have any questions, just ask.
I’m doing the problem right now and I got as far as subtracting the two latitudes but how did you did it?
Does anyone know how to do 109? I feel really stumped, and im not sure what variable to use to start
Nevermindd, i figured it out
So I’m stuck on 111 and 115 the angular speed part because I can’t find the central angles. SO how do you find them??
So because the wheel is making full rotations of 360 degrees it is really a hugee central angle. Because 2pi is equal to 1 rotation, or 360 degrees, you multiply 2pi by 5000(the amt of rotations) to get 10000pi as the central angle
Nevermind I think I figured it out
111 b) anyoneee? dont get it.
A little something I discovered while doing this weekend’s homework:
to get the grapher to “parametric” settings, go to mode, and switch functions to “par” (parametric).
another calculator question: does anyone know how to to the sec/csc/cot? whenever i did the inverse sin/cos/tan, I got a totally different answer.
I don’t know how to get the sec/csc/cot, but for the inverse sin/cos/tan, maybe your graphing mode is on radians or degrees (if it asks you to find the inverse of like 20 degrees, then your graphing mode has to be on degrees. if its on radians, then it would definitely screw up the answer.
Oh, disregard what I just said…i misread your question.
I meant is inverse sin/cos/tan the same as csc/sec/cot???
and if not, how do i get to csc/sec/cot? =/
Mariah, and all,
csc x = 1/sinx, not the same as inverse sine!!!
You can use the reciprocal button: x^(-1) or you can type the reciprocal directly: 1/sin(x) or you can use the power button: [sin(x)]^(-1).
All are equivalent.
Mode is important, as Jeff said. You want to check your mode and verify that it is in degrees if you are calculating degrees and radians if you are using radians.
Also, please note (for everyone) that I have reorganized your blog so that you can find the section you are working on and not have to go through so many posts to get there.
Hope it helps.
I was trying to do it before anyone posted for this section, but since I missed this chance, I “glumped” 1 and 2 together.
From now on, there will be one page for each section.
Take care and keep up the great work,
Mrs. Corricelli
hey sooo im just starting the homework for this weekend and i’m seeing some patterns in my answers. can anyone explain to me conceptually why the answers for 15, 19, 23 and 29 are so similar when t is for different values??
also- what is a “period” of a trig function??? how does that help you evaluate?
I don’t know if someone has already asked this but I’m having trouble using my calculator for numbers 49 and 55. I’m pretty sure I’m using the right mode but when I enter the problem into the calculator it keeps saying error. Does anyone have any solutions?
Rachel,
The answers are really similar because you are using the same triangle (30, 60, 90). And I think period is the same as arec length which helps you with t but I’m not sure.
Hey, so I’m just getting started on the homework… How do you find a point on the circle given t? I looked in the book but couldn’t figure it out… If anyone knows it would be really helpful.
I mean, without memorizing specific locations?
I hope this helps with the unit circle problems! Ok so to find points on the coordinate plane…if they give you
t = pi/6 for example,
i made it an angle on the unit circle, so that would be 30 degrees,
and then you have a 30-60-90 triangle
i used the triangle mrs. corricelli drew on friday for the lengths, so it would be
1/2 – (route 3)/2 – 1
and then you would find x and y by seeing where they lie on the triangle
evan- use the sin cos tan definitions for x and y we went over in class. ex: sint=y
wait so….. period=arc length?
Rachel/Colleen
I don’t think period is arc length…
On page 295, the book explains what a period is, and on page 296, it gives an example that walks you through how to use this information.
It’s kind of like finding the simplified sine and cosine. This will make sense when you look at those two pages.
One thing I realized while doing these problems…
When you’re given an amount (in the examples they are 13pi/6 and -7pi/2) as an answer you get some multiple of 2pi + pi/ an amount. The pi/ an amount (at least for the problems i’ve seen) has always been over the amount the given amount is. Like 13pi/6 is really 2pi+ pi/6. Both are over 6. Knowing that both will be over the same number gives you a starting point.
-In example 3 pg 296 you will see that in a) they are both over 6, and b) they are both over 2.
Sorry my explanation is probably confusing but if you read the book it will hopefully make some sense!
thank you haley that’s really helpful!
Thanks Haley your right and it helped me correct some mistakes I had made in my homework and sorry Racheal if I confused you.
Haley,Rachel, and Colleen,
Period is definitely NOT arc length.
Period is the length of “time” (may not always be time, but often is) it takes for a function to repeat itself. cos and sin “live” in a circle; they repeat every 2pi. That is why you can calculate sin(13pi/6) by calculating sin(13pi/6 – 2pi) = sin(pi/6). You can subtract or add 2pi as many times as you need to in order to get the number inside the trig function to be between 0 and 2pi, our “normal” unit circle window.
Arc Length is the distance you move around the circumference of a circle; it depends on the radius and the central angle and it need not be on a unit circle. This section (2) is about the unit circle.
Now: interesting connection. Arc length on the unit circle IS the same as the number of radians since angle measure in radians = distance covered moving around the unit circle as you change the central angle. 360 degrees IS 2pi since 2pi is covered on the unit circle when you rotate 360 degrees. This may be part of the confusion.
Thanks,
Mrs. Corricelli
Evan,
At this point, we can find a point on the unit circle for ONLY specific t values, increments of 45 degrees and 30 degrees and all rely on the 30-60-90 triangle and the 45-45-90 triangle covered in class. See the links on the main page (or under Honors Precalculus category) – it is my most recent post.
Thanks,
Mrs. Corricelli
Does anyone know how to do #37 on page 297? How do you evaluate the trigonometric function using it’s period as an aid? (cos7pi/3)
Never mind I figured it out
For number 11 on the homework, I’m getting all the right answers, except for finding tan of theta. if tan is opp/adjacent, then shouldn’t it be 1/ 2 rt 2 for the first smaller triangle? Maybe I’m doing this wrong, but I don’t know how I’m getting the other trig function evaluations right. thanks.
OHH nevermind, i forgot that I have to rationalize the denominator! oops