What is the solutions to y=sin(1/2 x)?

Question

Find all equation solutions in the interval [0, 2π). (Enter your answers as a comma-separated list. If there is no solution, enter NO SOLUTION.) Y=sin(1/2x)

Answer 1

Since in the x range of 0 to 2 pi sets y to sin 0 to pi, and in that range sin goes from 0 to 1 at pi/2 to 0 at pi, that is the graph in xy coordinates. Such a cure has infinite coordinates, but here are a few: (0,0), (pi/2, .707), (pi, 1.0), (3 pi/2, .707), (2 pi, 0).

Answer 2

-1 < y < 1 as sine of any angle is between -1 and +1 which is the range

y=sin(1/2x) with x in the interval [0, 2pi) = the domain

0< x < 2pi or 360 degrees

if you really mean sin(1/2x) and not sin((1/2)x) then x can't =0 as 1/2(0) = 1/0 which is undefined

domain of x is

x intercept are 1/4pi, 1/2pi

or maybe you meant sin((1/2)x) = sin.5x = sin(x/2)

the only x intercept is 0

then the sine is of an angle in the interval 0 < 0.5x < pi/2

sin0 =0, sin(pi/2) = 1

then

0 < y < 1

although it's possible or there's more information in the original problem

that narrows down the possible values of x and y more

maybe the original problem had a specific value for either x or y, such as Y=1/2, so it's askiing to solve for x

then (1/2)x = pi/6 or 30 degrees and x = pi/3

sin((1/2)pi/3) = sin((1/2)2pi/3) = Y = 1/2

solution for x is then pi/3, 2pi/3

or x = 60 degrees, 120 degrees

try graphing sin(x/2) or sin(1/2x)

with a graphing calculator