Find two values of 0, 0 ≤ 0 ≤ 2π that satisfy the following equation. Show your work.
sin 0 = 1/2
To find the values of θ that satisfy the equation sin θ = 1/2, we can use the unit circle or the trigonometric ratios for the special angles.
Using the unit circle:
The sine of an angle is equal to the y-coordinate of the point on the unit circle that corresponds to that angle. For sin θ = 1/2, we need to find the angles whose y-coordinate is 1/2.
In the unit circle, there are two points where the y-coordinate is 1/2: (0.5, π/6) and (0.5, 5π/6). These points correspond to the angles π/6 and 5π/6.
Using the trigonometric ratios for special angles:
We know that sin (π/6) = 1/2 and sin (5π/6) = 1/2.
Thus, π/6 and 5π/6 are the two values of θ between 0 and 2π that satisfy the equation sin θ = 1/2.
So, the two values of θ are π/6 and 5π/6.