Find the Exact Value sin(-(4pi)/3)

Problem

sin(−(4*π)/3)

Solution

1. Use the odd function property of the sine function, which states that sin(−θ)=−sin(θ)

sin(−(4*π)/3)=−sin((4*π)/3)

2. Find the reference angle for (4*π)/3 Since (4*π)/3 is in the third quadrant, the reference angle is (4*π)/3−π=π/3

Reference Angle=π/3

3. Determine the sign of the sine function in the third quadrant. In the third quadrant, sine is negative.

sin((4*π)/3)=−sin(π/3)

4. Substitute the known value for sin(π/3) which is √(,3)/2

sin((4*π)/3)=−√(,3)/2

5. Combine the results by substituting this value back into the expression from step 1.

−(−√(,3)/2)=√(,3)/2

Final Answer

sin(−(4*π)/3)=√(,3)/2

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