Question

for what value of on the interval (-9.65, 11.28) will f(x) take on a minimum if f(x)=−7.2sin(0.3x)+1.8cos(0.3x). What is f(x) at this x value? Same question for the maximum on the same interval.

Answer 1

this should say for what value of x on the interval... Sorry!

Answer 2

deriving trig...aint had to do this yet :)

Answer 3

well the derivative is -0.54sin(0.3x)-2.16(cos(0.3x) if you need it. I know I need to set it to zero to get the critical values, but I don't know how to solve for x lol

Answer 4

Dx(-7.2 sin(.3x)) = -7.2(.3) cos(.3x)

Answer 5

lol .... I was getting there :)

Answer 6

sorry! lol

Answer 7

lets multiply by 100 to get rid of some of those decimals

Answer 8

-54 sin(.3x) - 216(cos.3x) = 0

Answer 9

can we factor out anything from 54 and 216? I know 2 comes out...

Answer 10

you can take out a 9 i think

Answer 11

54/216 = 27/108..try 3 now 9/36 try 3 again 3/12 and 3 again 1/4

Answer 12

looks like 54 factors out completely...

216/54 = anything useful? 4 yay!!

Answer 13

-54(sin(.3x) + 4cos(.3x)) this look right to you so far?

Answer 14

yeah I'm following I think. lol, that's what I have when I do the same work on my calculator. :)

Answer 15

so, lets see what sin(.3x) + cos(.3x) gets us to equal 0

Answer 16

they gotta be opposites of each other, so lets throw one to the other side

Answer 17

and dont forget that 4 that I left out lol

Answer 18

yeah i was going to ask why we weren't using it, lol but nevermind

Answer 19

4cos(.3x) = - sin(.3x)

now picture these graphs for a minute

Answer 20

the cos is just stretched 4 tall, so the 4 doesnt matter

the sin is flipped over upside down

Answer 21

.3 = the frequency of the graphs

Answer 22

these cross points at 2 places every time they go thru one frequency...does that make sense?

Answer 23

once in Q2 and another in Q4

Answer 24

the only angle that has sin and cos equal is 45 degrees

Answer 25

right.. I put them in my graphing calculator. lol so that means I have more than one answer right?

Answer 26

yes... more than one answer, and it will have something to do with 45 degrees

Answer 27

-9.65 and 11.28 is our interval

Answer 28

.3(sqrt(2)/2) = ?

Answer 29

.2121320344

Answer 30

I might be wrong about the 45 tho :)

Answer 31

derive it again to see if we can get some useful information...

Answer 32

derive the original f(x) or take the second derivative?

Answer 33

second derivative will give us a better picture....

Answer 34

64.8 sin(0.3 x)-16.2 cos(0.3 x)

Answer 35

I got:

y'' = .648 sin(.3x) - .162 cos(.3x)

Answer 36

oh, yeah I just had it multiplied by 100 still

Answer 37

it might be helpful, but im still "stuck" :)

Answer 38

When I asked a friend, she told me I needed to use the quadratic. However, she had her math major friend do the problem for her, and can't tell me anything farther than that lol

Answer 39

lets go back to the original..

sin(.3x) + 4cos(.3x)

Answer 40

Is there a way for us to write them both in the same terms, like a way for us to make cos to sin?

Answer 41

there can be a square root involved, or a phase shift....

Answer 42

sin = sqrt(1-cos^2)

Answer 43

sin^2 = 1-cos^2

Answer 44

If it helps, when I tried using wolfram alpha, it gives me the answer.. x = 20/3 (pi n+tan^(-1)(1/4 (1+sqrt(17))))

Answer 45

oww...my eyes.....

Answer 46

But I don't actually even know what that means, lol so I that wasn't very helpful either. It was kind of a a last resort as it was, because my assignment is due at midnight. :\ lol

Answer 47

4cos(.3x) = -sin(.3x)

square both sides to get

16cos^2(.3x) = sin^2(.3x)

16cos^2(.3x) = 1 - cos^2(.3x)

Answer 48

then:

17cos^2(.3x) -1 = 0 right?

Answer 49

i believe you're correct.

Answer 50

cos^2(.3x) = 1/17

Answer 51

cos(.3x) = sqrt(17)/17 then ....if that helps :)

Answer 52

okay so x ends up being like 4.419392212

Answer 53

cos-1(sqrt(17)/17) is?

Answer 54

cos-1(sqrt(17)/17) is 1.325817664 i think

Answer 55

25.32 is what I get for that x :) does that make any sense?

Answer 56

25.32 radians of course

Answer 57

ohh.. so why am I getting a different number, is my calculator just in the wrong mode?

Answer 58

maybe; and I used 1/sqrt(17) to be simple

Answer 59

lets plug that in to see what we get:

sin(.3(25.32)) + 4cos(.3(25.32)) :=: 0 ??

Answer 60

I'm not getting zero. :\

Answer 61

0.1321 + 3.9648 = .... ack!!!

lol.

Answer 62

need someone smarter than me I guess :)

Answer 63

oh no. lol what do I do now? Do you have any ideas of where else I can get help b y midnight?

Answer 64

how many points it take off if it is wrong?

Answer 65

I'm not sure.. there are only 4 sections and this one is technically two parts.

Answer 66

let me review our stuff for a few minutes and see what I can deduce...

Answer 67

alright. If it helps, on the thread for the problem, it says to take the derivative equal to zero, and that you should get tan=#, then take the inverse.

Answer 68

I don't know how they're getting tangent though.

Answer 69

What if we divided both sides by cos(0.3x) and then had tan(0.3x)=4.. does that work?

Answer 70

-4x -y=0...-y=4x....-y/x = 4

-4x +y = =..... y=4x......y/x=4

this is the tan they get at....

-sin(.3x)
------- = 4
cos(.3x)

-sin(x) = sin(-x) so thats the same

Answer 71

tan(a) = 4

tan-1(4) = what?

Answer 72

i was getting to it.... :)

Answer 73

75.96 degrees is a divide that by.3

Answer 74

so we have 253.212=x ?

Answer 75

that sounds large. lol

Answer 76

remember that tan-1 spits out an angle between -90 and 90

Answer 77

(75.96 + 180) /.3 ?? maybe

Answer 78

(75.96 - 90)/.3?

Answer 79

that one gives us -46.8

Answer 80

i see that..... maybe our interval itself gives us a max or min at the end points?

Answer 81

if you put those in.. for -9.65, we get 0.0119783705 and for 11.28, we get -0.190832377

Answer 82

.3x gives us one cycle every 20pi/3 does that helps us out?

Answer 83

well in the wolfram alpha, it said something about 20/3 pi * n, but n is supposed to mean any integer, so I didn't really understand it.

Answer 84

n = the angle measurement

a normal cycle is 2pi

but we disturb that with .3.... so it increases the frequency of the cycle to 20pi/3

Answer 85

6 and 2/3 pi

Answer 86

x = 20/3 (pi n+tan-1(1/4 (1+sqrt(17))))

Answer 87

What is the value of our interval in terms of pi?

Answer 88

x(pi) = -9.65

x = pi/-9.65

Answer 89

-.325 pi to .279 pi right?

Answer 90

that aint gonna make a difference, becasue our interval is telling us the value of "x" which is the angle involved.... not the period....

Answer 91

okay.. I'm just lost at this point. lol I really don't even know how to get any further in this.

Answer 92

im at a loss for the moment as well :) its all those decimals that are messing me up

Answer 93

I've got it!!!! lol I graphed it and just followed the graph and put in the numbers :P thanks though hahah