Question

value of cos x - sqrt(3) sin x > 0, if ....

Answer 1

@3mar @zepdrix

Answer 2

@agent0smith

Answer 3

The answer is
\[\frac{ \pi }{ 12 } < x < \frac{ \pi }{ 6 }\]

Teach me how to get that

Answer 4

@Kainui

Answer 5

Hello!

Answer 6

How are you?

Answer 7

I'm fine :)
u?

Answer 8

I am fine.
Thank you!

Answer 9

glad to hear that!
can u help me solve this problem?
I need to solve it quickly

Answer 10

@FaiqRaees

Answer 11

Let me try

Answer 12

ok thx :)

Answer 13

Is this the problem
\[ \cos x - \sqrt[3]{\sin x}>0 \]

Answer 14

\[\cos x - \sqrt{3} \sin x > 0\]

Answer 15

oh okay
start by taking the sin x term on right side

Answer 16

Yes it looks like what Kevin has just typed

Answer 17

well, like what?

Answer 18

tp be like that
\[\cos(x)>\sqrt{3}\sin(x)\]

Answer 19

*to

Answer 20

then?

Answer 21

Divide sqrt3 cos x on both sides

Answer 22

then divide the two sides by cos(x)

Answer 23

\[\frac{ \cos(x) }{ \cos(x) }>\sqrt{3}\frac{ \sin(x) }{ \cos(x) }\]

Answer 24

1 > sqrt(3) tan x

Answer 25

divide sqrt 3 on both sides

Answer 26

to be:
\[1>\sqrt{3}\tan(x)\]

finally you got the form:
\[\tan(x)<\frac{ 1 }{ \sqrt{3} }\]

Answer 27

ok....

Answer 28

Idk but, my book said tan x = -sqrt 3

Answer 29

What is the domain we can get the answer in?

Answer 30

there is no domain

Answer 31

Can you share the answer procedure?

Answer 32

of your book?

Answer 33

it's too long

Answer 34

wait

Answer 35

Take your time.

Answer 36

To be aware of what the result be, this is a graph of it.
sorry it will be that:
https://www.desmos.com/calculator/9yohdvzrq3

Answer 37

pls wait

Answer 38

Your book answer is wrong. Take for example the angle -23. The tan of -23 is -0.424 which is smaller than 1/sqrt 3. And the cos (-23) - sqrt3 sin(-23) = 1.59

Answer 39

23 degrees ~ -2/15 radians

Answer 40

Let's check firstly, FaiqRaees

Answer 41

http://prnt.sc/cuw3pn

Answer 42

How did the book interchange between inequality sign and equal to sign in the fifth step?

Answer 43

it's not done yet. here is the second page :
http://prnt.sc/cuw5ej

Answer 44

I will translate it

Answer 45

No Okay I got it. I made a slight easier approach wanna hear?

Answer 46

btw I always lost connection, I must refresh everytime I post something here. Ok I glad to hear that

Answer 47

Okay we know that cos pi/2 and cos 3pi/2 =0
Which means we can write
cos (x-2pi/3) = cos pi/2
And cos (x-2pi/3) = cos 3pi/2

Right?

Answer 48

where did you get cos pi/2 and cos 3pi/2 ?

Answer 49

take the arc cos of 0. You will get pi/2 and 3pi/2

Answer 50

Sorry, but where did you get arc cos of 0?

Answer 51

Can you draw the graph of cos x

Answer 52

I mean on the question, it's not said that cos x = 0

Answer 53

Oh that. We are taking the extreme values possible. By that we can work out the boundaries

Answer 54

Its like if I say what are the values of x for which f(x)>0. By working out the value of x at which f(x)= 0, you can easily tell for which values of x is f(x)>0 (Considering f(x) to be increasing function)

Answer 55

Hmm.... ok, I'll study it further xD
continue your answer explanation

Answer 56

How about this
cos (x-2pi/3) = cos pi/2 And cos (x-2pi/3) = cos 3pi/2
Where did you get that?

Answer 57

Can you understand till the fifth step in your book

Answer 58

no xD

Answer 59

how about u?

Answer 60

Well they first convert the expression into the form
kcos (x-a)
Clear?

Answer 61

no

Answer 62

I don't see the relation

Answer 63

o_O

Answer 64

wait 2 minutes.

Answer 65

ok

Answer 66

@3mar any idea?

Answer 67

Btw you dont understand how kcos(x-a) was arrived?

Answer 68

it's from cos x = cos a

Answer 69

am I right? ._.

Answer 70

No no. You haven't studied the angle addition formula?

Answer 71

Owhh... I got it, it's from a cos x + b sin x
I never teached by my teacher about different trig sum

Answer 72

if u know what I mean

Answer 73

yes its from that

Answer 74

then how did second line on my book come from?

Answer 75

I mean third line- fourth

Answer 76

Yeah the answer in your book is wrong
https://www.wolframalpha.com/input/?i=cos+x+-sqrt3+sin+x+%3E0

Answer 77

For the answer to be pi/12 and pi/6, the value of n in the real solution has to be 11/24 and since n belongs to the set of integer it cannot have the value 11/24

Answer 78

But, your answer is not provided on the options, is it?

Answer 79

No the answer I mentioned pi/12 and pi/6 were given by your book

Answer 80

Owhh... ok, anyway let's using my book way cos I learned from it xD
I've know line 1-4 now. How about fifth line?

Answer 81

This is a question from a test that given by my government to selected the student who want to go a college. That's why it's not teached intensively in my school.

Answer 82

I'm understand now, thx guys!

Answer 83

value of cos x - sqrt(3) sin x > 0, if ....

if what??? Where's the rest of the question??

Answer 84

@FaiqRaees @3mar you should not divide both sides by cos x, since you do not know if it's positive. You can't do it w/o affecting the truthiness of the inequality.

Answer 85

That's the question @agent0smith
I've figured out the answer, thx for u reply :)