using the figure, establish the value of function y=sin0 when 0=pi/3
To determine the value of the function y = sin(0) when 0 = π/3, we need to look at the unit circle.
The unit circle is a circle with a radius of 1 and centered at the origin (0,0) on a Cartesian plane. We can divide the circle into 4 quadrants, each with a central angle of π/2.
In this case, we are considering an angle of 0 = π/3, which falls in the first quadrant. We can see that this angle intersects the unit circle at a point with x-coordinate equal to cos(0) and y-coordinate equal to sin(0).
Additionally, we know that the cosine of an angle is equal to the x-coordinate on the unit circle, while the sine of an angle is equal to the y-coordinate on the unit circle.
So, when 0 = π/3, the x-coordinate is cos(π/3) and the y-coordinate is sin(π/3).
Looking at the unit circle, we can see that in the first quadrant (0 to π/2), the x-coordinate is positive (√3/2) and the y-coordinate is also positive (1/2).
Therefore, when 0 = π/3:
cos(π/3) = √3/2
sin(π/3) = 1/2
Hence, the value of the function y = sin(0) when 0 = π/3 is 1/2.