Finding solutions for sin on a unit circle.

Hi!

I was confused with this.

I have to find all the solutions for 0__<__x__<__360^{o} if sinethreex=(square root2)/2

So I was confused with this.

I know (square root2)/2 occurs in 45^{o}, also pi/4

Then it occurs at 135^{o}, also 3pi/4

I'm not sure if these 2 are the correct solutions.

I understand where sin (the y coordinate) is (sqrt2)/2

But I'm not sure what the sinethreex means.

Can someone explain.

Re: Finding solutions for sin on a unit circle.

If then

So, you will have six solutions, two for each of the 3 revolutions about the unit circle.

Can you find the remaining 4 solutions?

Re: Finding solutions for sin on a unit circle.

Quote:

Originally Posted by

**MarkFL2** If

then

So, you will have six solutions, two for each of the 3 revolutions about the unit circle.

Can you find the remaining 4 solutions?

Um, are we supposed to multiply the 0__<__x__<__360 by 3? o.o

Cause the problem says "Find all solutions for 0__<__x__<__360" if sin 3x = (square root of 2)/2

But yeah, the other 4 is pretty obvious then :)

390^{o}, 495^{o}, 750^{o}, 855^{o }Thanks :O

Re: Finding solutions for sin on a unit circle.

Multiplying the restriction on *x* by 3 shows you what the corresponding restriction on 3*x* is, which is the argument for the sine function.

Re: Finding solutions for sin on a unit circle.

Re: Finding solutions for sin on a unit circle.

Quote:

Originally Posted by

**MarkFL2** No, for the next 2, add

to

and

, then divide by 3 to find

*x*:

And then for the last 2, add

to

and

and then divide by 3.

Oh wow, I accidently added the wrong degrees to some of them xD, but thanks :)

Re: Finding solutions for sin on a unit circle.

Quote:

Originally Posted by

**Chaim** I have to find all the solutions for 0__<__x__<__360^{o} if sin3x=(sqrt2)/2

Substituting cos(3x) by its equivalent in complex plane we need to solve:

for z=x+i y and then they are all the principal solutions 0-2pi. We obtain 6 roots as follows: