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H Pre Calculus Ch. 6
Happy New Year! Get off to a great start by doing your homework.
Mrs. Johnson's 2015-2016 BC Calculus Students ROCK!
1/6/2011 10:32:23 am
have you guys done 89, 92, 95, or 98 in the homework? cause i don't quite understand how you are able to find out what theta is and how to find the 6 trig functions...its on page 394
1/6/2011 12:09:25 pm
for those problems i drew a coordinate plane with all the quadrants and then i plotted the points. then you have to find the hypotenuse with the pythagorean theorm. after that you are able to find the exact values of the 6 trig functions...hopefully that helps
1/6/2011 12:11:34 pm
101 and 104 anyone?
1/6/2011 12:57:44 pm
Actually, you don't even have to draw a coordinate plane. With the given points, you can get the hypotenuse and once you have that, you can start solving for the six trig functions. Remember that sine goes with the y part of the coordinate and cosine goes with the x part. So for example:
1/9/2011 10:14:49 am
Does anyone know how to do problem number 102?
1/9/2011 01:33:40 pm
1/11/2011 08:13:56 am
Can anyone explain the difference between linear speed v. linear velocity problems? Is there are a difference in solving them? And also, what is the difference between angular speed and angular velocity. Which one does v=rw apply to?
1/11/2011 09:13:46 am
I'm having problems with setting up problem 89 in 6.1's second assignment. I know I should work backwards (starting with the linear speed equation and work backwards to the angular speed) to get the answer, but whenever I try to solve for theta I get a really weird fraction that makes no sense in context with the problem. Does anyone know how to do this problem?
1/11/2011 09:31:52 am
Kayla: I'm not entirely sure, but I think linear speed and linear velocity are actually the same thing, just worded differently. In the same way, this also applies to angular speed and angular velocity. But I'm positive that v=rw is for linear speed and velocity. You use it only when you found out w, which is angular velocity, or (theta/time).
1/11/2011 10:35:25 am
89. Ok, so we know that linear speed is 9.55 miles/hr and the diameter is 8.5 ft.
1/11/2011 10:37:24 am
1/11/2011 10:40:43 am
Hey I know the answers to number 88 on 6.1 are on the syllabus, but can someone explain to me how exactly to figure it out? I cant really figure it out. Thanks
1/11/2011 10:49:05 am
Hey vish I can help with you the first part of #88:
1/11/2011 11:15:18 am
1/11/2011 11:19:47 am
sorry, in the third line that's supposed to say "approach."
Beatrice Koka !
1/12/2011 07:48:54 am
ayee! so i was wondering if anyone know hknows how to convert radians to feet? for problem #86 in section 6.1 im not sure how to convert radians to feet because i already found the linear speed which is "pie(radians)/35secs" so after that you would multiply that times 30ft (because the equation w= vr.
1/12/2011 09:03:16 am
Hey guys! What did you get as the answer to number 30?
1/12/2011 11:02:42 am
for angular how do you change radians to the correct unit? like problem 6.1 # 76? <(") penguin
the mattinator is matt latham
1/12/2011 11:05:51 am
1/12/2011 11:06:26 am
1/13/2011 01:51:38 am
I can help with number 76:
1/19/2011 12:08:58 pm
1/19/2011 12:20:05 pm
**Yes I know that the teacher teaching in the videos is a hardcore perfectionist, but bear with her, it really helps.
1/19/2011 01:30:09 pm
Can anyone help me with the limit problem on the worksheet? I feel like I'm over-thinking it. It says what is the limit as x approaches cos(theta) from the right and left. Thanks!
1/19/2011 01:31:58 pm
Forget that, I meant "what is the limit of cot(theta) as x approaches zero from the left and right". My mistake.
1/19/2011 01:58:59 pm
It really helps to look at the graph of cot on a calculator, then you can clearing see what it is talking about. But if you cannot, try drawing the graph out by making a t-chart and you can see that as the graph approaches 0 from the left it is going to negative infinity and from the right it is going to infinity
1/20/2011 05:47:54 am
Can someone tell me how to graph cot, csc, and sec on the caclulator to check my work? I forgot how to do it
1/20/2011 09:27:45 am
I don't think that there is an actual button for cot, csc, and sec functions on the calculator. But for cot, you could type cos(x)/sin(x) into the calculator. For csc, you could type in 1/sin(x). And for sec, you could type in 1/cos(x).
1/20/2011 10:33:30 am
To Sejzelle: Okay so this is basically the same thing as James said, but to make things really easy, when it says what is the limit of cot(theta) as x with a negative sign, then you know that it will be from the left, and if it has a plus sign then you know that it will be from the right. Knowing this, use your finger and from the far LEFT OR RIGHT, trace it till you get to that spot and see what the value is at that specific point. In the instance of cot, if it is coming from the right (positive) then it will always be positive infinity, and from the left side (negative), it will be negative infinity.
1/20/2011 11:57:02 am
I agree with Chandan
1/22/2011 06:12:27 am
On 6.3 #73-78, how do you solve the problems without using a calculator. For example, 73 is sin^2(40)+cos^2(40) and 40 degrees is not on the unit circle...
1/23/2011 03:41:31 am
To Kayla: This problem at first may look confusing and not make sense, but you have to remember the pythagorean identities, which in this case you should utilize sin^2(theta)+cos^2(theta)=1. THIS IS CRUCIAL to remember in order for you to do this problem. Comparing the appearance of the identity and #73, wich is sin^2(40)+cos^2(40), you see the similar form. *you do not need the "theta" to make it able to be solved*. So in this case, the answer is just 1. It's that simply.
1/23/2011 03:50:24 am
I should have asked this before, but I need help on #s 75-78 in 6.3. How would you solve those; it says not to use the calculator and 80 degrees is not defined on the unit circle...
1/23/2011 03:54:15 am
NEVER MIND THAT QUESTION. I just figured out that one of the terms is just a reciprocal so the answer for all 5 is wither 1 or 0. Sorry about that.
1/23/2011 04:43:00 am
The last line is supposed to say "either"...NOT wither. My bad.
1/23/2011 02:05:11 pm
1/24/2011 10:33:52 am
Ok so Mrs. Johnson was not here today and she gave us a review packet to do in-class. There was one problem which I copied down and I need help understanding it:
1/24/2011 10:36:13 am
Also, it is true that in order to find the horizontal shift of a trig function, you have to solve for the x if the there is a number in front of the "x"?
1/24/2011 01:30:53 pm
1/24/2011 01:39:15 pm
Could someone please help me with the mathematical explanation on the worksheet that we got for homework tonight? I'm really confused.
1/24/2011 01:43:44 pm
1/24/2011 02:14:27 pm
hey guys im just doing some review problems from sections 6.4-6.5. the problem says y=cot(x+ pi/8). I understand how to graph the problem and i know u wud shift it over to the left pi/8 and the period would still be 2 pi, but im just confused on how i would label the x axis on the graph.
1/24/2011 03:00:34 pm
I am stuck on the worksheet too, but I think that the mathematical explanation might have something to do with the fact that the Range equation has sin(2theta) and when you plug in 45, you get sin(90)=1, which is the largest sin value in the first quadrant. But I'm not sure how to explain it for the Height equation.
1/24/2011 03:51:38 pm
For the worksheet, did anyone else get that the 45 degree angle maximized the range.
1/25/2011 09:10:24 am
If you plug in the equation that the worksheet gave you on your calculator, you can check the range in the stat plot to check your answers
1/25/2011 10:09:48 am
1/25/2011 01:12:50 pm
To Sohaila: Ok, remember that for the tangent and cotangent graphs' periods, YOU ALWAYS divide the term in front of the x by pi, not 2pi. What I do for labeling any of the graphs is I just put it starting it off with pi/2, then pi, then 3pi/2, 2pi, etc. Then I just visualize the original graph of the function, and knowing that I use the transformations and graph.
1/25/2011 01:13:30 pm
Hey guys when in the first problem y=5sin(4x) what does the 4 do. I know that the 5 changes the amplitude of the graph.
1/26/2011 08:48:18 am
To Maddie: Whenever there is a number in front of the x term, this defines the period of the function. For sin, csc, cos, and sec, you divide 2pi by the value, so here it is sin, so the period will by pi/2. BUT for tan and cot, you divide by pi instead of 2pi. You are right about the amplitude, but the 4 defines the period...hope I helped.
1/26/2011 02:16:07 pm
If anyone can answer the following questions I have related to the test on Friday, that would be great:
1/27/2011 08:01:28 am
Hi I was studying for tomorrow's test and one thing that I really need help on is when you know the linear speed and you need to find the angular speed. I can find the linear speed with the angular, but not opposite.
1/27/2011 08:08:18 am
Can someone please explain the projectile problems in 6.3 in simplest terms...? I am just completely stuck by those right now.
1/27/2011 08:36:43 am
Anika: Linear speed is when you find how much distance is traveled per unit of time (seconds). Angular speed is basically how many radians/degrees are covered per unit of time.
1/27/2011 09:22:51 am
This is for #71 for the review problems towards the end of the chapter. How is the answer pi/3...? Shouldn't this problem follow the rule for s=r(theta)? If you apply it here the answer turns out to be 60 feet. It is asking for the length of the arc.
1/27/2011 10:09:18 am
1/27/2011 10:17:57 am
1/27/2011 10:23:00 am
1/27/2011 10:31:24 am
And i just want to make sure. When you are trying to find out the phase shift of a graph and there is a coefficiant before the x value, so for example the problem says y=3cos(pix - 2)+1, you take the pix - 2 and set it equal to zero and solve for x.
1/27/2011 10:41:30 am
Could someone help me with #26 from the review? the question is find the exact value of tan-20/tan200
1/27/2011 11:56:06 am
Ashwin, I could not have asked for a better explanation...you really cleared things up for me; you have absolutely no idea. One question for you though: what do you type into the calculator, or exactly what does this mean...for sin^2(THETA)?? is it basically sin of the value, and then you square it? I'm trying that but it's not working.
1/27/2011 12:11:27 pm
Thanks chandan! Also, if when graphing an equation and you find that the period is in radians but the right or left shift is not, then how do you label the x-axis. would u convert one of them so that it is specifically either in radians or whole integers?
1/27/2011 12:16:42 pm
1/27/2011 12:32:27 pm
Yea Sohaila, basically like Shivani just said. YOU ALWAYS LABEL THE X AXIS BASED ON THE PERIOD!!! if it is in terms of pi, then label in intervals of pi, but if just a normal integer, then label it using normal numbers.
1/27/2011 01:20:01 pm
For number 49 in the review, y=-2tan(3x) how would you label the x axis? i know the period is pie/3.
1/27/2011 01:46:34 pm
Alex: it would start at zero, and then go to pi/6, pi/3, etc, I believe.
1/27/2011 02:34:42 pm
1/27/2011 02:37:23 pm
If anyone is still awake, could you please help with number 63 in the recioew problems? It's not part of the homework. I just wanted to know how you would figure out which points to put on the x-axis?
1/27/2011 03:46:06 pm
In the 6.1-6.2 quiz on the back page what is the answer to 4a. I know you can not distribute the cosine... so what are you supposed to do to find the solution.
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Mrs. Johnson teaches math at Metea Valley High School in Aurora, IL.