Question

trig problem.. help pls

Answer 1

\[f(\theta) = \frac{ 1 - \cos \theta}{ 4\sin \theta - 3\cos \theta + 6 }\]

Answer 2

?

Answer 3

\[\theta \epsilon \mathbb{R} \]

Answer 4

prove that for the all values of theta
\[0 \le f(\theta) \le \frac{ 6 }{ 11 }\]

Answer 5

i don;t even have slightest clue for this problem... :/

Answer 6

@dumbcow , @agent0smith , @phi @Hero , @ganeshie8 , @ehuman pls help

Answer 7

@ranga

Answer 8

so it must be a cyclic, so can't you find the maximum and minimum to give you the limits,

Answer 9

huh ?

Answer 10

I know i have to fimd max and min but how ?

Answer 11

who wants a medal and a fan ? give me one ill give you one ^_^

Answer 12

Find f'(theta) and set it to 0. Solve for theta. Those will be the critical points (meaning potential max/min points).

Answer 13

do you know calculus ?

Answer 14

that's the problem... I don't know calculus yet

Answer 15

i mean i haven;t learned anything under the topic calculus. but I think we have learned the base for calculus...

Answer 16

according to my knowledge...
i think that both numerator and denominator should contain the same trig function in order to calculate the max and min... i mean it was the base for the ones i've solved.. but none of them were in the form of a division...

Answer 17

With a graphing calculator I can see that the statement is true, but I don't know how to evaluate this manually.

Answer 18

hmm well the old fashion way is plot points using unit circle, that will give you idea of graph and turning points....then plug in other values near turning points and you should see a trend toward min of 0, max of 6/11

Answer 19

but how can i prove this ? dumbcow

Answer 20

Plot

Answer 21

the proof is that limit of slope of tangent line goes to 0......hence derivative and calculus :{

Answer 22

I have to get to class, later.

Answer 23

the irony is that calculus is what gives us the proof

Answer 24

I can teel you that thr roots are at +2pi(k) k = innterger

Answer 25

I don't know whether this will help u guys to get an idea..
but so far the problems i've solved in this exercise were linear ones..
so all i had to do was turn all sin , cos, tan value in to a one form .. then get the answer..
so i think this one has to be solved in the same way... but this is a division.. so I can't guess wt to do :/

Answer 26

i guess i;m on my own in this problem... anyway thank u guys :/

Answer 27

you can also use a calculator to find the max and min values, doesn't require calculus.

Not sure if there's an easy way to simplify that original function, though

Answer 28

http://www.wolframalpha.com/input/?i=f%28%5Ctheta%29+%3D+%5Cfrac%7B+1+-+%5Ccos+%5Ctheta%7D%7B+4%5Csin+%5Ctheta+-+3%5Ccos+%5Ctheta+%2B+6++%7D

^ none of the alternate forms are helpful

Answer 29

So w/o calculus i'd think you'd need to use a graphing calc.