How to solve sin(3x)= 1/2 ?

Question

nubeer · Answer

replace 3x=y

sin(Y) = 0.5
now find the angels for y.. can u do that?

anonymous · Answer

i got x = pi/18

anonymous · Answer

is that the right answer?

nubeer · Answer

yes .. but this is one angle.. you have to find the other angle too.

anonymous · Answer

How do I find that? The problem doesn't specify a restriction, so do I have to find the infinite  number of angles?

nubeer · Answer

no.. not infinite.. 
it's like this.. 
sin(3x) =0.5 
you have to look after the equal sign whether it's positive or negative , in this case it's positive.. so you have to see in which quadrants the value of sin is positive..

1st and 2nd quadrants.. in both of these the value of sin is positive..

nubeer · Answer

3x = pi/6

so pi/6 is in first quadrant.. so you have to find the angel for second quadrant too..
that you can find by pi-pi/6

3x = pi , 5pi/6

now solve it

anonymous · Answer

Don't you mean 3x = pi/6, 5pi/6?

anonymous · Answer

I got pi/18 and 5pi/18

nubeer · Answer

yup.. exactly.

nubeer · Answer

i was just explaining incase you didn't knew...

anonymous · Answer

Okay, thank you!
I have one more question, could you help me with that?

nubeer · Answer

yup sure..

anonymous · Answer

tan2x = 1 in the interval [-π/2, 3π/2]

nubeer · Answer

ok.. so have you started solving this?

anonymous · Answer

I started with 2x = 1, so 2x = π/4 and 5π/4. I just don't get what the restriction means

nubeer · Answer

the restriction tells that you have to tell all the angles between that range..

for that you have to know in which quadrants tan is positive.

anonymous · Answer

Quadrants I and III

nubeer · Answer

yes and any of these quadrants comes between the range defined in question?

anonymous · Answer

What does  [-π/2, 3π/2] mean? It makes one revolution, but doesn't that mean I can't say π/4 and 5π/4?

nubeer · Answer

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nubeer · Answer

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