Verified answer

2x= pi/4 + k2pi ---> x = ..... , k in Z

2x= 3pi/4 + k2pi ---> x = ....

sin2x-?2/2=0 pass the sq. root over sin 2x = ?2/2 if the sine of an attitude is sq. root of two over 2, then the attitude could be pi/4 (40 5 ranges) or 3pi/4 (a hundred thirty five ranges). so 2x = Pi/4 or 2x = 3pi/4 x= pi/8 or 3pi/8 it particularly is the easy answer in case you agree for solutions basically interior the 0 - 360 degree selection.

Move the number to right side

you have sin 2x = 0.707

The angles of 2x should be (45 degrees +360 N )

or Pi/4 +2Pi N

and (135 degrees + 360 N)

or 3Pi/4 +2Pi N

Therefore x= Pi/8 + Pi N

or X=3Pi/8 +Pi N

sin2x = sqrt(2)/2

sin is sqrt(2)/2 at pi/4 and 3pi/4

so 2x = pi/4 3pi/4

x = pi/8 3pi/8

all solutions are pi/8 +2pik and 3pi/8 +2pik

sin2x= √2/2

sin45°=√2/2

x=22.5°

This is sin(2x) =(√2)/2. You should already know that sin(π/4) and sin(3π/4) equal (√2)/2. So that means 2x = π/4 ± 2πn, or 3π/4 ± 2πn for any integer n, which means x = π/8 ± nπ, or 3π/8 ± nπ.

sin(2x) = (sqrt(2) / 2) occurs for 2x at π/4, 5π/4, 9π/4, 13π/4...

So x = π/8, 5π/8, 9π/8...as well as -3π/8, -7π/8,...}

Therefore the answer is:

{ x | x = (π/8) + (k*(π/2)) where k is any integer - negative, 0, or positive}

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