Find the Exact Value sin(-(2pi)/3)

Problem

sin(−(2*π)/3)

Solution

1. Apply the odd function identity for sine, which states that sin(−θ)=−sin(θ)

sin(−(2*π)/3)=−sin((2*π)/3)

2. Determine the reference angle for (2*π)/3 Since this angle is in the second quadrant, the reference angle is π−(2*π)/3=π/3

Reference Angle=π/3

3. Evaluate the sine of the reference angle. The sine of π/3 is a known value from the unit circle.

sin(π/3)=√(,3)/2

4. Determine the sign based on the quadrant. Since (2*π)/3 is in the second quadrant, its sine value is positive.

sin((2*π)/3)=√(,3)/2

5. Substitute the value back into the expression from step 1.

−sin((2*π)/3)=−√(,3)/2

Final Answer

sin(−(2*π)/3)=−√(,3)/2

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