Question

How many solutions does the equation sin(5x) = 1/2 have on the interval (0, 2PI]

Answer 1

Well, if you take a 30/60/90 triangle you get:


Therefore, when theta = 30 you get 1/2.

30 degrees = pi/6

Now then, you have to deal with the sign.

They are positive in:



You would be correct in the first and second quadrants.

pi/6 and 5pi/6

So 2 times.

Answer 2

case I :
sin5x=1/2
sin5x=sinpi/6
5x=(n*2pi+pi/6)
x=(n*2pi/5+pi/30)
just check for n=0,1,2,...
case II :
sin5x=1/2
sin5x=sin5pi/6
5x=(n*2pi+5pi/6)
x=(n*2pi/5+pi/6
and again u must check for n=0,1,2,3,...
which x's satisfied in interval (0,2pi]

Answer 3

so..twice?

Answer 4

RadEn What are you doing?

Answer 5

yeps.. but sometimes there are duplicate number for x, so u just take once

Answer 6

what do u mean @malical

Answer 7

I don't know why you have N's.

Answer 8

ohhh, it is a identity for trigono equation ^^

Answer 9

sin5x=sinpi/6
5x=(n*2pi+pi/6)

Why don't you just take the arcsin of each?

Answer 10

er

Answer 11

because the question to find "how many....."
i think we didnt need arcsin of each, becasue we can get by manual to find for x's

Answer 12

I'm stepping out of Spectrum's question and looking at your word directly.

Answer 13

work* rather

Answer 14

nopes.. @malical
dont forget this one, one of identity for sin :
sin x = sin(n*2pi + x)

Answer 15

That is stupid. You are just adding 2pi which is a full circle. That's fine and all, but it isn't needed.

Answer 16

have u tried it ?? @malical
be carefull for this case :
5x=(n*2pi+pi/6)
x=(n*2pi/5+pi/30)
now, i give some examples for u.
for n=0, it means x=pi/30 (satisfying for interval (0;2pi])
n=1, it means x=2pi/5+pi/30=13pi/30 (right too :p)
.
.
.
and so on, until u meet no satisfied of x in interval (0,2pi]

Answer 17

What that means is that if you go around the unit circle (2pi) once you get the same answers. n2pi just means more unit circles. That is what the identity is. Example:

sin[6pi]
Is the same thing as sin[3(2pi)]
And 2pi=0

So you get Sin[0].

Answer 18

oke, i see that
lets make a new question:
sin2x=1/2 (x in interval [0,2pi]
find the value of x ?

Answer 19

pi/12 and 5pi/12

Answer 20

what ur answer @malical

Answer 21

oke, i will demonstrate it for u @malical
sin2x=1/2
case I :
sin2x=sin(pi/6)
sin2x=sin(n*2pi + pi/6)
2x=n*2pi + pi/6
x=n*pi + pi/12
if n=0, then x=pi/12
if n=1, then x=pi + pi/12 = 13pi/12 (still satisfied)
if n=2, then x=2pi + pi/12 = 25pi/12 (not satisfied)
so on, for n=3,4,5,... not satisfied in interval (0,2pi]
case II :
sin2x=sin(5pi/6)
sin2x=sin(n*2pi + 5pi/6)
2x=n*2pi + 5pi/6
x=n*pi + 5pi/12
if n=0, then x=5pi/12
if n=1, then x=pi+ 5pi/12 = 17pi/12
if n=2, then x=2pi+ 5pi/12=25pi/12
so on, for n=3,4,5... not satisied in interval (0,2pi]
so, there are 4 solution

Answer 22

the solution are :
pi/12 , 13pi/12 , 5pi/12 , and 17pi/12

Answer 23

well, @spectrum...
i hope u can finish ur problem like i done

Answer 24

i want to going to masque, know
good luck .... Byeee

Answer 25

*now

Answer 26

It is 2. Because if it is x from 0 to 2pi that would work. But it is 2x from 0 to 2pi. So it is only 2.

Answer 27

The other two would be -1/2

Answer 28

sin2x
if i plug x=13pi/12 gives
sin(2*13pi/12) = sin390 degrees = sin30=1/2 not -1/2
looks raden is right

Answer 29

yea, for x=17pi/12
sin(2*17pi/12) = sin510 degrees = sin150=1/2 too

Answer 30

so how many are there ._.

Answer 31

oh btw..it wasn't 4 ..it was 10 -.-

Answer 32

4 was from my question, not ur problem @Spectrum :p

Answer 33

note to self...do not skim for answer at 6:00 in the morning without sleep for awhile

Answer 34

so, do u want its specific's answer

Answer 35

i already got it wrong but you can help on my current question if you like it lolz

Answer 36

haha... ok, what isit