Find the Exact Value sin((7pi)/6-pi/3)

Problem

sin((7*π)/6−π/3)

Solution

1. Find a common denominator for the fractions inside the sine function to simplify the argument.

(7*π)/6−π/3=(7*π)/6−(2*π)/6

2. Subtract the fractions to find the simplified angle.

(7*π)/6−(2*π)/6=(5*π)/6

3. Identify the position of the angle (5*π)/6 on the unit circle.

(5*π)/6=150

4. Determine the sine value for (5*π)/6 which is in the second quadrant where sine is positive.

sin((5*π)/6)=1/2

Final Answer

sin((7*π)/6−π/3)=1/2

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