find all solutions of the equation in the interval [0,2pie) 2sinx- squre root of 2 =0

Answer 1

Beginning with this equation:

2sin(x) - √2 = 0, add √2 to both sides to get 2sin(x) = √2 .

Divide both sides by 2 to get sinx = (√2)/2 .

This means that we're looking for places on the unit circle where the y coordinate = (√2)/2.

The two places where this happens are at π/4 and 3π/4.

Your answer looks like this: x= π/4 , 3π/4 .

Remember, the (x,y) coordinate of an angle on the unit circle is equal to the (cos, sin) of that angle.

Have fun, and let me know if you need any help!

-LizZ

Answer 2

2sinx-√2=0

2sinx=√2

sinx=√2/2

look on the unit circle

sin=√2/2 at ∏/4 or 45° and at 3∏/4 or 135°