Question

Find all solutions of the equation
sin(x) = 1 / 2
in the interval [0 , 2π) and explain the solutions graphically using a unit circle and the graph of sin (x) - 1/2 in a rectangular coordinate system of axes.​

Answer 1

Answer:

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Answer 2

Step-by-step explanation:

sin(x) is positive in quadrant I and II and therefore the given equation has two solutions.

In quadrant I, the solution to sin(x) = 1 / 2 is x = π / 6. (green in unit circle)

In quadrant II, and by symmetry of the unit circle, the solution to sin(x) = 1 / 2 is x = π - π / 6 = 5π/6 (brown in unit circle)