The little "r thing" in trigonometry is the radian measure of an angle.
Using the radian measure of 7π/6, we can evaluate the sine function as follows:
sin(7π/6) = sin(π - π/6)
Using the identity sin(π - θ) = sin(θ), we can simplify this to:
sin(7π/6) = sin(π/6)
The sine of π/6 is 1/2, so we have:
sin(7π/6) = 1/2
Therefore, sin(7r/6) = 1/2 when r is measured in radians.