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

## Answer this Question

## Related Questions

- Pre-Cal (Please help) - Find all the soultions of the equation in the interval...
- Pre-Cal(Please check) - 1) Find all the solutions of the equation in the ...
- Pre-Cal(Please check) - 1) Find all the solutions of the equation in the ...
- Math - Find the solution. 1. sqrt2 sin x + 1 = 0 My ans: x = 5pi/4 + 2npi and ...
- Math - 1. On the interval [0, 2pi] what are the solutions to the equation ...
- Precalculus check answers help! - 1. Which expression is equivalent to cos ...
- Pre Cal---Fix to the question below - Let P be the point on the unit circle U ...
- trig - 1. 3cot^2 (x) - 1 = 0 My answer: pi/3, 2pi/3, 4pi/3, 5pi/3 2. 4cos^2 (x...
- Pre-Cal(Please check) - Approximate the equation's solutions in the interval (0,...
- Pre Cal. - 1. Use half-angle identity to find the exact value of cos165. MY ...

More Related Questions