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What is the value of 
sin((5pi)/(6))?
Choose 1 answer:
(A) 
-(sqrt3)/(2)
(B) 
-(sqrt2)/(2)
(c) 
(1)/(2)
(D) 150

What is the value of sin(5π6)? \sin \left(\frac{5 \pi}{6}\right) ? \newlineChoose 11 answer:\newline(A) 32 -\frac{\sqrt{3}}{2} \newline(B) 22 -\frac{\sqrt{2}}{2} \newline(C) 12 \frac{1}{2} \newline(D) 150150

Full solution

Q. What is the value of sin(5π6)? \sin \left(\frac{5 \pi}{6}\right) ? \newlineChoose 11 answer:\newline(A) 32 -\frac{\sqrt{3}}{2} \newline(B) 22 -\frac{\sqrt{2}}{2} \newline(C) 12 \frac{1}{2} \newline(D) 150150
  1. Identify angle and sine value: Identify the angle in the unit circle and its corresponding sine value.\newlineThe angle (5π)/6(5\pi)/6 is in the second quadrant where sine values are positive.
  2. Recall sine values for common angles: Recall the sine values for common angles in the unit circle.\newlineThe sine of π6\frac{\pi}{6} is 12\frac{1}{2}, and since 5π6\frac{5\pi}{6} is a reference angle to π6\frac{\pi}{6} in the second quadrant, its sine value will be the same but positive.
  3. Determine exact value of sin(5π6)\sin\left(\frac{5\pi}{6}\right): Determine the exact value of sin(5π6)\sin\left(\frac{5\pi}{6}\right).sin(5π6)=12\sin\left(\frac{5\pi}{6}\right) = \frac{1}{2}

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