Question

Find all degree solutions:
2sin^2 3Ө + 3sin3Ө+1=0

Answer 1

let\[u=\sin\theta\]then try to factor it

Answer 2

\[2\sin^2 3Ө + 3\sin3Ө+1=0\]
let \[\sin3 \theta = x\]

Answer 3

^^^
sorry, that's what I meant ;)

Answer 4

It would give 2x^2 + 3x +1=0

Answer 5

so let x=sin3theta right ?

Answer 6

so after that what do i do ?

Answer 7

theta=pi/2,7pi/6,11pi/6,.....
and5pi/12,13pi/12,....

Answer 8

please explain it in degrees thanks :)

Answer 9

2x^2 + 2x +x +1
2x(x+1) +1(x+1)
(2x+1)(x+1) = 0
x=1/2 or x= -1

Answer 10

Then sin 3theta = x
sin3 theta= 0.5
theta = sin3^-1 times 0.5
which equals 9.55366

Answer 11

i just explaineed

Answer 12

now for all the answers, you first need to subtract from 180 degrees that answer, and add to 180 degrees that answer, and subtract from 360 degrees that answer.

Answer 13

wait what? all of that for multiple answers ? how do i know which one to add 360 and which not?

Answer 14

can't i use quadratic formula to get x ?

Answer 15

yes, but you have one answer, and then you need to subtract it from different degrees to get all the answers.

Answer 16

is 30 and 90 are some of the answers ?

Answer 17

90 and 75 are 1 of the anwer

Answer 18

I'm not sure
If we have multiples, such as cos(2x), then we also multiply up the possible number of solutions. In "general", as a rule of thumb, expect the following, within any 360 degree range:

sin(x) --> 2 solutions
sin(2x) --> 4 solutions
sin(3x) --> 6 solutions
sin(4x) --> 8 solutions
sin(5x) --> 10 solutions etc

http://www.algebra.com/algebra/homework/Trigonometry-basics/solving-trigonometric-equations.lesson

Answer 19

so in this case it could have up to 6 solutions ?

Answer 20

Yes. Just check more sites to see how to solve it for sin3x

Answer 21

so did you found out all the answers ?

Answer 22

if i found 90 is one of the answer do i take 180 and subtract it or something?

Answer 23

No, I forgot it wasn't sin2x until I went to this site... so I forgot the range you need to subtract and add to.. I'm sure sahii knows.

Answer 24

@sahil51993 come here :D

Answer 25

i used quadratic and i got x=-.5 and x=-1 =.=

Answer 26

we got sin3x =-1 or -1/2
now we know that sinx is -1 for 3pi/2 and so on +2pi
and sinx is -1/2 when angle is 5pi/4 and so on hence we can equate these to 3x and find the requied value of x in terms of pi and later put pi=180 degrees to calculate the answer

Answer 27

@sahil51993 so we put -1=3x and -1/2=3x just solve for x ?

Answer 28

no we put sin 3x=-1 and sin 3x=-1/2

Answer 29

@sahil51993 after that can't i just use Sin inverse to get the answers?

Answer 30

sin^-1(-1/3) and sin^-1(-1/6) ?

Answer 31

@sahil51993 i got -19.47 and -9.5

Answer 32

yes u can but do take all the possibilities

Answer 33

@sahil51993 so do you take sin^-1(1/3) and got 19.47 and take that 19.47+180/3 to get answer or what? please help me pleaseee

Answer 34

sorry for keep bothering you, but i really need help >.<

Answer 35

nopes 1/3 sin^-1 (-1) gives 1 value as 270/3 as sin^-1(-1) is 270 and so on 1/3 sin^-1 (-1/2) gives 1 value as 225/3 as sin^-1(-1/2) is 225 and so on

Answer 36

oh you gotta put 1/3 in front ok

Answer 37

wait 1/3sin^1(-1) does not give you 270/3 wth

Answer 38

i got -30 from that

Answer 39

it does sinx=-1 for 270,630,990,.......

Answer 40

no....my calc, oh wait you don't put it in calc ?

Answer 41

no i can calculate it mentally

Answer 42

i tried it in the calc but it does not give me that

Answer 43

I got 1 thing wrong sin ^-1(-1/2)=210,570,930,.....

Answer 44

that give me -30 =.=

Answer 45

i dont understand what im doing wrong :|

Answer 46

u can say that because sinx is an odd function so sin-30=-sin30 so yes but this seems incorrect in practical life where u cannot represent answer in negative vale actually ur question is not proper it should as us value of theta in a particular range......get it....and i have my exam day after tomorrow so please make it quickly

Answer 47

oh sorry, ok just one more thing, please explain how you got from 270 to 630 to 990 what did you do ?

Answer 48

sinx=-1 for 270 and again when it completes a peroid and comes back to -1 value is increased by 360 and so on

Answer 49

ok i got it thanks!!