Math help

[Adam]

I need help with a math problem.
I have solved an equation like this:

2sin(3x + 18) = 2^½ 
sin(3x + 18) = (2^½)/2 = sin(45) 
1/sin(sin(3x + 18)) = 1/sin(sin(45)) 
3x+18 = 45 
3x = 45-18 = 27 
x=9

My teacher said that there should be more solutions and that I should take the domain in consideration.
The domain is: 𝟎≤𝒙≤𝟑𝟔𝟎

I hate and suck at trigonometry, help is really appreciated

[Neoxter]

yeah its easy,

sin(x)=sin(x+2kpi) // k is an integer; 0,1,2..n

that's it

[Adam]

Originally Posted by Neoxter

yeah its easy,

sin(x)=sin(x+2kpi) // k is an integer; 0,1,2..n

that's it

Thanks
But could you explain how you got that answer?

[Neoxter]

the forumula i gave is a general formula. u can try it on a calculator if u forget formals (that's what i do )

for example :
sin(30)=0.5 | k=0
sin(30+360)=0.5 | k=1
sin(30+ 720)=0.5 | k=2
and so on.. this applies in the above formula, note that the above formula is in radians

if u want to use degrees, which is ur domain 0<x<360 ( eza radians bekoun 0<x<2*pi )

pi(radians)=180 degrees

so the formula for degrees is sin(x)=sin(x+360*k) k is an integer

in ur given problem :

sin(45)=sin(3x + 18)
u put : 45=3x+18
which only gives u the value of k=0 from my formula but in fact there are more solutions
now apply my formula

3x+18=45+360*k

x= (360*k + 27)/3

x=120*k + 9

now u substitute all values of k such that u obey ur domain.

k=0 ~> x=9
k=1 ~> x=129
k=2 ~> x=249
k=3 ~> x=369
which is not in the domain, and so for all values of k=>3

so the solution final solution is

x=9 x=129 x=249

i can't make it any more clear :P

[Adam]

OK, now another problem

I tried to solve the equation like this:

0.5*sin2x=-cosx
0.5*2*sinx*cosx=-cosx
sinx*cosx=-cosx
sinx=-cosx/cosx=-1
sin^-1(-1)=-90
180-(-90)=270
x=270

My teacher told me that I can't divide by cosx since cosx might equal 0.
And now I'm stuck

[J()e]

0.5*sin2x=-cosx
0.5*2*sinx*cosx=-cosx
sinx*cosx+cosx=0
cosx(sinx+1)=0
cosx=0 and sinx+1=0
x=pi/2+kpi and x =3pi/2+2kpi

I think mazbouta

[Neoxter]

u can transform sinx to cosx , i think the formula is sin(x+90)=cos(x)

now u have sin on both sides, proceed as above

i thought u are in university man :P

what are u studyin and what course is that?

[Adam]

Guys I think there is a difference between the symbols you use in Lebanon and the one I use.
What do you mean by pi, do you mean 3.14... or is it something else? Cause I'm looking through my book and the isn't a mention of it.

Originally Posted by Neoxter

u can transform sinx to cosx , i think the formula is sin(x+90)=cos(x)

now u have sin on both sides, proceed as above

If you look at the first post you'll see that I said I suck at trigonometry, let me rephrase that: I suuuuuuuuuuckkkk.
Please show step-by-step cause otherwise I'll just get more confused

Originally Posted by Neoxter

i thought u are in university man :P

what are u studyin and what course is that?

I am, I'm right now taking a couple of physics and maths courses because the school I was studying at thought it'd be better if we focus on things like history and Swedish rather than the more important physics and maths. As a result, I can't start the normal university courses until I'm done with maths and physics.

[J()e]

^
yes pi=3.14...

and about neo's method , I would not recommend it because yimkin tghalbit bi chi formula,i think the way that i solved the problem is the best way to deal with such problems.

NB: Your teacher was telling you that your answer is valid for every x different from (2n+1)pi/2...

[Adam]

Last one

Calculate tanv exactly, if sinv =-0.2 and v is in the third quadrant.

I have no idea how to start.