Question

the measure of angle is 7π/6. the measure of its reference angle is *blank* degrees, and sin is *blank*.

Answer 1

The measure of angle θ = 7pi/6. To convert this to degrees, substitute pi with 180 degrees. Pi is always equal to 180 degrees.
θ becomes: 7 x 180/6
Therefore, θ = 210 degrees.
And, to solve for sin θ, you can directly input sin (210) in the calculator. 
Thus, sin θ = sin (210) = -0.5 or -1/2

Answer 2

$\dfrac{7\pi}{6}\times\dfrac{180\°}{\pi}=210\°$

$\sin\left(\dfrac{7\pi}{6}\right)=\sin\left(210\°\right)=-\dfrac{1}{2}$