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

Problem

sin(−(3*π)/4)

Solution

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

sin(−(3*π)/4)=−sin((3*π)/4)

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

Reference Angle=π/4

3. Determine the sign of the sine function in the second quadrant. Since sine is positive in the second quadrant, sin((3*π)/4)=sin(π/4)

sin((3*π)/4)=√(,2)/2

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

−sin((3*π)/4)=−√(,2)/2

Final Answer

sin(−(3*π)/4)=−√(,2)/2

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