Question

Cos2x + 2sinx = 0

Answer 1

I need help will anyone help?

Answer 2

What do you want to do ??

Answer 3

What is your question??

Answer 4

This is the simple equation you have written..

What we are to find here ??

Answer 5

I am assuming that you have to find sinx here..

Answer 6

\[\cos(2x) = 1 - \sin^2(x)\]

So:

\[1 - 2 \sin^2(x) + \sin(x) = 0 \implies 2\sin^2(x) - \sin(x) - 1 = 0\]

Answer 7

Waterineyes I have a question how come the -2sin^2x becomes positive?

Answer 8

Here you can factorize it:

\[2\sin^2(x) - 2\sin(x) + \sin(x) - 1 = 0 \implies 2\sin(x)(\sin(x) -1) + 1(\sin(x) - 1) = 0\]

\[\sin(x) - 1 = 0 \qquad Or \qquad 2\sin(x) + 1 = 0\]

Answer 9

@Brendan97 I have multiplied by (-1) both the sides..

Answer 10

No no no... see I have to find all solutions in the interval from 0 to 2pie , buyt I can't see yourt responses... and oh... I am a little slow sorry

Answer 11

I have to find all solutions and they are all crazy solutions like 5.908, and 3.516
How do I acquire that.. I am a frshman taking pre-calc and I have no teacher so I struggle.. if you could slowly explain the steps plz

Answer 12

you there?

Answer 13

\[\cos(2x) = 1 - 2\sin^2(x)\]

Answer 14

Yes I know that double angle identity so I understand that , but the soltuions shown on my paper I don't understand how to get any of them

Answer 15

So plug this in place of cos(2x)..

Answer 16

I explain you wait..

Answer 17

\[\sin(x) - 1 = 0 \qquad Or \qquad 2\sin(x) + 1 = 0\]

Can I explain after this ??

Answer 18

alright well I have all that and then I use quadratic formula and I get 2 (+ or -) sqrt12 / 4

Answer 19

Why you get those solutions and not quadratic formula?

Answer 20

there is no need to use quadratic formula..

We can use factorization here..

Answer 21

I show you by quadratic formula so that I can check you are correct or not.

Answer 22

but your solutions are not what my papre shows.. quadratic formula gives me 1 plus or minus the square root of 3 divided by 2

Answer 23

\[2\sin^2(x) - \sin(x) - 1 = 0\]

\[\sin(x) = \frac{1 \pm \sqrt{9}}{2 \times 2} \implies \sin(x) = \frac{1 \pm 3}{4}\]

Answer 24

My answers for this questions are:

A) 5.908,3.516
B) 4.084, 1.726
C) 5.908
D) 1.726

Answer 25

Water how you get square root of 3? In my quadratic equation A = 2 B= -2 C = -1? HBY?

Answer 26

Therefore:

\[\sin(x) = 1 \qquad Or \qquad \sin(x) = \frac{-1}{2}\]

Answer 27

My answers for this questions are:

A) 5.908,3.516
B) 4.084, 1.726
C) 5.908
D) 1.726

Answer 28

Which answer is it then?

Answer 29

B is -1 and not -2..

Answer 30

how?

Answer 31

2sin^2x - 2sinx -1 = 0 is the problem

Answer 32

\[2\sin^2(x) - \sin(x) -1 = 0\]

Answer 33

no see you must have accidently gotten the wrong problem.. it's cos2x + 2sinx = 0

Answer 34

Sorry then I have to write it again..

Answer 35

Just wait..

Answer 36

yeah it's okay I wish we had msn so we could reply faster

Answer 37

\[2\sin^2(x) - 2\sin(x) -1 = 0\]

\[\sin(x) = \frac{2 \pm \sqrt{12}}{4} \implies \sin(x) = \frac{1 \pm \sqrt{3}}{2}\]

Answer 38

Yup that is exactly what I have :) Now how do I use that to get these answers>?

My answers for this questions are:

A) 5.908,3.516
B) 4.084, 1.726
C) 5.908
D) 1.726

Answer 39

Wait let me check first..

Answer 40

water are you in pre-calc?

Answer 41

I am in college..

And I am not generally study these things..

I had read them 4 years back..

Answer 42

oh.. uhm well this sucks .. see once you get that anxswer you have to find which one it is and I can never find and help so today I discovered this website hoping for help... looks like I am stuck for ever

Answer 43

:/

Answer 44

See we can separate this like:

\[\sin(x) = \frac{1 + \sqrt{3}}{2} \implies \sin(x) = 1.366\]

\[\sin(x) = \frac{1 - \sqrt{3}}{2} \implies \sin(x) = -0.366\]

Answer 45

Now we have to find x here..

Answer 46

Yeah but solutionsa re solutions to sin(x) , but the x is these numbers... the answer is some degree measurement on the unit circle but I can't figure out how to calculate . opnline it says 1.366 cannot be possible because it;'s outside but some measure of .366 is our answer

Answer 47

where ever sinx = .366 I think not sure?

Answer 48

gg this is so depressing .. no one can help me.. I have no damn teacher and I just wana quit.. :'( FFS

Answer 49

You there? If not.. this is just bs L.

Answer 50

Wait..

Answer 51

alright sorry I am just depressed I have been wroking for weeks on this question and my course ends soon I am gonna faikl :/

Answer 52

First one is not possible..

Answer 53

Water the first one :

My answers for this questions are:

A) 5.908,3.516
B) 4.084, 1.726
C) 5.908
D) 1.726

A is the answer

Answer 54

I need to know how to do it so I acan advance in life..

Answer 55

Go with second:

\[\sin(x) = -0.366 \implies x = -21.48\]

Answer 56

The answer is the first one.. , but I have no idea how to find it... I found answer online somewhere

Answer 57

See you can write it now as:

\[\sin(x) = -\sin(21.48)\]

Answer 58

Let me try first with full my satisfaction..

Answer 59

hmm?

Answer 60

\[\sin(x) = \sin(-21.48) \implies \sin(x) = \sin(-0.12 \pi)\]

Answer 61

I have converted degree into radians..

Answer 62

Water but that is not the right answer :/

My answers for this questions are:

A) 5.908,3.516
B) 4.084, 1.726
C) 5.908
D) 1.726

Answer 63

\[\large x = n \pi + (-1)^n (-0.12 \pi)\]

Answer 64

Here put n = 1 here and find x..

Answer 65

?

Answer 66

I got 3.51628 on putting n = 1 here..

Answer 67

3.519 close where you get that formula?

Answer 68

These are the general formula I will give you the link I have given tutorial on this topic today only..

Now put n = 2..

Answer 69

n = 2 gives me 6.245 u?

Answer 70

5.9032..

Answer 71

i show you I think you messed up with negative sign there..

Answer 72

how you type in calc? I type 1(Pie) + (-1)^1(-.012pie)

Answer 73

\[x = 2\pi + (-1)^2 (-0.12 \pi) \implies 2 \pi - 0.12 \pi = ??\]

Answer 74

I am doing normally with my mobile..

Answer 75

yeah, but how you do that for 1?

Answer 76

wait 2(pie) =6.283

Answer 77

\[\large x = \pi + (-1)^1 (-0.12\pi) \implies x = \pi - (-0.12 \pi) \implies \pi + 0.12 \pi\]

Answer 78

-.12(Pie) =.377

Answer 79

Check it for 2pie @Brendan97 you are doing mistake in calculation I guess..

Answer 80

Where is negative sign ??

Answer 81

5.906 for 2(pie)( and 3.519 for 1 :) Is that correct?

Answer 82

Yes it is correct..

Answer 83

but how did you come up with that random formula and apply it to my problem?

Answer 84

http://openstudy.com/updates/5018d167e4b04dfc808c85e1

Try to study every part here..

Hope this will add something to your knowledge..

Answer 85

wait can you just explain

Answer 86

I have explained everything there please read once on your own..

Here its 2:21 in the morning..

Answer 87

all I see is like code for color blue and stuff?

Answer 88

all I see is like code for color blue and stuff?

Answer 89

it's not displaying properly

Answer 90

Reload your page and then see..

Answer 91

There check the Second Form (1) that is explaining your formula..

Answer 92

same it's says like color red theta and stuff... ugg :/well this was no help... can I get like that fiormula?

Answer 93

how did you get that .12(pie) at that end of the formula?

Answer 94

I have converted -21.48 to radians by multiplying it with pie by 180..

Answer 95

how did you get -21.48?

Answer 96

\[-21.48 \times \frac{\pi}{180} \implies -0.12 \pi\]

Answer 97

Can you retype me that formula?

Answer 98

\[\sin(x) = -0.366 \implies x = \sin^{-1}(-0.366) = -21.48\]