Question

still trigonometric equations ._.

Answer 1

Find all solutions to the equation.

7 sin2x - 14 sin x + 2 = -5

Answer 2

@Luigi0210 yay your on! will you help?

Answer 3

Start by setting it equal to 0.

Answer 4

7 sin2x - 14 sin x -3 = 0

Answer 5

Actually, add 5.. remember you do the opposite operation. So \(7sin^2x-14sinx+7=0\), isn't that easier? Now factor~

Answer 6

7(sin^2x-2sinx+1)
7(sinx-1)(sinx-1)

Answer 7

Nice job :)
Don't forget to have that =0 at the end, or else it's just a random expression and not an equation.

And right away, you can divide that constant 7 away.

Answer 8

aww my ketty dosent show up :c and oh okay and i already did get rid of the seven

Answer 9

I'm sorry >.<

But yea, that leaves us with \((sinx-1)^2=0\)
Can you finish it?

Answer 10

isnt that it .-.

Answer 11

Nope, solve for x

Answer 12

i have no idea how .-.

Answer 13

Take the square root of both sides \(sinx-1=\sqrt{0}\) then get sinxx= by itself \(sinx=1\), now where in the unit circle does \(sinx=1\)?

Answer 14

at the - sqrt of 0?

Answer 15

Where did \(-\sqrt{0}\) come from? \(\color{red}{ლ(ﾟдﾟლ) }\)

Answer 16

well you said sinx−1=√ 0 is the same as sinx=1 so i asumed you just added the 1 to each side and subtracted √ 0

Answer 17

Yes, but 0 doesn't add any value so it just disappears.
Do you know your unit circle?

Answer 18

Here's a good one
http://ibmathematics.tripod.com/sitebuildercontent/sitebuilderpictures/unitcircle.gif

Answer 19

btw. for trig the coordinate points are \((cosx, sinx)\)

And y u be leavin me? \(\large \color{#00FFCC}{ლ(ﾟдﾟლ) }\)

Answer 20

(ノಠ益ಠ)ノ彡┻━┻
my computer shut down, and holy crap what is THAT

Answer 21

That would be the unit circle my dear~
You haven't seen it yet?

Answer 22

lanope.... you told me about the whole rotating counter clockwise and i already knew that a circle was 360degrees

Answer 23

Yes, and \(360^○=2\pi\)

Answer 24

i get that they are fractions, but where are the points coming from?

Answer 25

30-60-90 and -45-45-90 triangles..

Answer 26

\(\large \color{#00FFCC}{ლ(ﾟдﾟლ) } \quad \color{blue}{\text{Looking Nice..:)}}\)

Answer 27

Thanks xD

And sorry, I'm not good at teaching :( @lovelyharmonics

Answer 28

i think you are c: you are one out of only three people i ask for help on here XD

Answer 29

Trying to be flattery @lovelyharmonics ?? :)

Answer 30

say wat? 【・ヘ・?】

Answer 31

Hehehehe...

Answer 32

Thanks.. and you can make that 2 soon because I'm gone later :P

Saw what? o.O

Answer 33

nonono you not your an abasitor or administer person thus you must stay

Answer 34

LOL

Answer 35

I'm just a regular user like you and most everyone else >.<

Answer 36

naw on your profile thats not what is said

Answer 37

oooooooooooooooooo

Answer 38

Wait, why are we talking about this on a question form? >.<

Answer 39

wait so how do i figure out where it goes on the circle?

Answer 40

IDK

Answer 41

Look for where sinx=1

Answer 42

90degrees?

Answer 43

Yup, I'm not exactly sure how to write it in radian terms tho..

Answer 44

To convert degree into radians just multiply it by pi/180..

Answer 45

so its pie/2

Answer 46

It is one solution only..

Answer 47

^I know that, but there is no interval.. I mean like how would you write it with no interval.. is it something like \(\frac{\pi}{2}+2\pi n\)?

Answer 48

General Solution??

Answer 49

YES, general solution.

Answer 50

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

Answer 51

Let us go there now..

Answer 52

\[\sin(x) = \sin(y) \implies \color{red}{x = n \pi + (-1)^n y}\]