Test date

Is the test for chapter 8 still on friday?

Assignments 9 and 10

I did both of them, but I heard that 3rd period doesn't have them due until Tuesday. Are they due today?

tExpand() and tCollect()

The functions tExpand() and tCollect() are located in the Algebra menu in the Trig sub-menu. tExpand() will expand functions such as sin(2x) to 2sin(x)cos(x). Someone apparently didn't program half angles in apparently, because sin(x/2) will not expand. The opposite function, tCollect(), will take a function such as 2sin(x)cos(x), and give you back sin(2x).

Clarification for solving quadratic type problems.

SO the basic method is to do the quadractic formula for the problem and then do inverse funtion of whatever you chunked? help please

8.4 73

It says that tan x + 5 is a factor, so when you factor this equation, you get (tan x + 5)(4sin x -3). From here you can take the inverse tan of -5, and the inverse sin of 3/4. This should give you the right answers.

section 8.5 #59

How would u do the proof for arcsin(-x)=-arcsin(x) ? I don't understand how the chunking method would work for this problem either.

Review pk. 11-15

Does anyone have review problems 11-15? Apparently they are not on Mr. Karafiol's website. If anyone has the assignments, send to silliewillyzg@yahoo.com

Solution to 85

i figured if you change 4cos^2x by dividing 4 on both sides and chagne cos^2x to 1-sin^2x, you can cross moultiply then factor to get the answer.

questions on 8.4 73 & 81

for 73, i am not seeing where the 1.2059 + k*pi value for tan x came from. Could someone help me w/ this.

Also, for 81, am i not allowed to say sin^2(x) + 3*cos^2(x) = 0 is the same as
1 - cos^2(x) + 3*cos^2(x) = 0, which changes to 1 - 2*cos^2(x) = 0, and in turn simplifies to cos (x) = +/- (sqrt(2))/2. This would indeed have a solution, as opposed to the book. Would someone support this?

Solution to 8.4.51

The problem reads as follows:

cot x = 2.3
We know that cot x = 1/tan x so we can re write the equation.

1/tan x = 2.3
1=2.3(tan x)
1/2.3=tan x
Arc tan x (1/2.3) = .4101
There for the solutions for the equation are + or - .4101 + pie*n

*It can also help to chunk tan x after re-writing the equation as 1/u = 2.3 (tan x = u)

review probs 11-15

did we get the review problems for assignment 10? if we did i cant seem to find them, so please email them to me:
coolcat791@gmail.com

thanks

homework due 2/26

i know we have been changing a lot of the homework lately and i was just confuzed about wut the hw due mon is

Cos3x...

im not sure if i did it right i thought it was too long.
i did
cos(2x+x)
cos2x*cosx-sin2x*sinx
(cosx*cosx-sinx*sinx)*cosx-(sinx*cosx+cosx*sinx)*sinx
(cosx^2-sinx^2)*cosx-2(sinx*cosx)*sinx
(cosx^3-sinx^2*cosx)-2(sinx^2*cosx*sinx)
....ido alot more but does it look like i started right?
im pretty sure theres a faster way.

8.3.40

for this one, i'm not sure if i did it the right way.
sin4x = 4sinx*2cosx = 3.84
is this the way you're supposed to do it?

Solution to 8.3.45

sin(2x)/2*sin(x) =
(2*sin(x)*cos(x))/2*sin(x)=
(sin(x)*cos(x))/cos(x)=
cos(x)

hope that helps..

assn 8, no. 5

i know this problem is insanely simple, however i keep doing it and my answer doesn't seem to be right. anyone care to explain?

Help with 8.3.49 and 50

Can someone plz explain to me how to do these two?

#50

Does anyone have any suggestions for this problem? I don't know where to start.

Tutoring

I said this before but now it is official. Anyone who is in third period lunch and needs math help, I am starting to tutor officially. If anyone else needs help, on Fridays I tutor in Mr. O'roark's room. If anyone needs tutoring help on other days, I know of other people in our class who are tutoring on different days and if you just don't want MY help , there are other people on Fridays. I may be the only one third period though.

8.3 #43

I definitely had to go back and re-try this problem several times before getting the right solution, so here are some hints in case you get stuck:

cos3x = cos(2x +x) = cos2xcosx - sin2xsinx

sin2x = 2cosxsinx

cos2x= 2(cos^2)x - 1

If you substitute these expressions for sin2x and cos2x, it makes simplifying much easier, because you can factor cosx out of both terms. (I tried the other expressions that also equal cos2x and they only make the problem more complicated.)

Also, later on in the simplifying process, it might help to remember that (cos^2)x-(sin^2)x = cos2x.

Hopefully this might help a little.

assignment 5 & review problems

i know this is a little late, but if anyone could tell me how to begin proving number 54, that would be great. also, i see that people have already asked about this, but did we ever learn how to find the volume of a pyramid based on the angle of elevation and/or what does Re(z) mean?

review sheet

For number 3 I see the patterns but i dont know how to put it in words for part D. and in #4, i am really confused as to what the formula for the paramid is and for #5, i dont understand the last part, like what is Re(z).
melissa

Review sheet # 5

For part c) how do u do absolute value again? Is that the one u use the formula for pythagorean theorum on?

Re(z) means the real part of z

Re(z) means the real part of z

Undef Graphs

If the graph of two functions is both all undefined are they an identity?

8.1.57 and means-extremes

In # 57, where does the use of multiplying the top and bottom by sin x come into play?
Also, could it be assumed that means-extremes always works?

review problems #4

can anyone explain how to get the height of the pyramid in terms of t degrees for number four?

thanks

review sheet 3b

You can rewrite 1+2=2^2...+2^9 as 2^0+2^1...+2^9 and that sum=2^10. Why does this work?
I don't get the connection between a and b/c.

Chap. 8 Review Problems

2d. Is "an expression for f'(x)" any different from "a simplified expression for Df(x)"? Don't f'(x) and Df(x) both refer to the IRC? Or is f'(x) more specific (i.e. does it not have an "h" in it)? I put -.01x+.16 as my simplified expression for f'(x) because that was the equation I got when I drew the tangent on the graph of f(x) at x=6. I don't know if this is right or not.

4. I honestly have no idea where to begin. Any ideas?

5e. I am confused about what this question is asking. What does "Re(z)" mean? Is it asking us to find the remainder when (z + conjugate of z) is divided by two? And in that case, why would it say "prove"?

Thanks.

Radians

OK, so does anybody have a clever way to remember the radians at each angle around a circle as posted in our book, or do i basically just have to memorize them?

17b solution

My idea for 17b is that maybe we could use the cos 42 as a ratio for the diameter of the earth at 42 deg. north. Upon finding cos 42, multiply by 8000 to get the new diameter, and multiply that by pi for the new circumference. Dividing by 24 gives an answer of 778 mph. Maybe someone can back me up on this.

14 on pretest

Is one of the answers for this poblem -2? if not, what is the other solution or solutions. i think i understand, but i'm not as confident in this answer.

pretest # 17

b. I would think that it would have the same linear velocity as part a, but obviously it doesn't. How do u use the angle measurement to figure this problem out?

Problem 18 of the Pre Test

Problem 18 is a clever and interesting problem. The way to solve it is by finding a common denominator by multiplying the denominators together. This will give the expression:

1(1 - sin x) + 1(1 + sin x)
___________________ =

(1 - sin x)(1 + sin x)

Now simplify:

2 /(1 - sin x + sin x - sinx^2 x)2 = 2/(1 - sin x) = 2/(cos^2 x) = 2 sec ^2

Am i overthinking #19, or is the answer simply (a+b)? If tan(x) = sin(x)/cos(x) and tan here is (a+b)/(a-b), can i just assume that sin is (a+b) and cos is (a-b)?

Also, I agree with Sam about 17b and with Carrie about 25.

Pretest # 17 b

Don't even know where to start.

pretest #24 and 25

I tried to do both problems and made very little progress. For 24 I started by graphing y=2^sec(x). The graph is periodic and contains vertical asymtotes. However, I wasn't sure how to interpret that into a domain and range. Any suggestions? Also, for 25 I really didn't know where to start. Can you say k=sin(x)? Is that even worthwhile?How do you incorporate the 1:5 ratio?

Easy way to do pretest #22

To do this problem, simply graph y=3^cos(x) . Now, set the viewing window to [0,2pi] and simply find the minimum of that window to get the answer.