Posted by **Hannah** on Wednesday, February 17, 2010 at 11:25am.

Find all the soultions of the equation in the interval (0,2pi)

sin 2x = -sqrt3 /2

sin -sqrt3 /2 is 4pi/3 and 5pi/3 in the unit circle

2x= 4pi/3 + 2npi 2x=5pi/3 + 2npi

I do not know what to do at this point.

- Pre-Cal -
**Damon**, Wednesday, February 17, 2010 at 2:56pm
30, 60, 90 triangle

1, sqrt 3,sides and 2 hypotenuse

sin A = + (sqrt 3)/2 if A = pi/3

so

if A = pi + pi/3 which is 4 pi/3

or

if A = 2 pi - pi/3 which is 5 pi/3

then sin A = -sqrt(3) /2 {AGREE}

But A = 2x

so

x = 2 pi/3 or 5 pi/6

Now if they mean x can be as large as 2 pi we better look for bigger angles for A

Like A = 2 pi + 4 pi/3 = 10 pi/3

then x = 5 pi/3

and

Like A = 2 pi + 5 pi/3 = 11 pi/3

then x = 11 pi/6

which is still less than 2 pi (barely

so

I get four values for x total

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