Find the Exact Value sin(-(5pi)/4)

Problem

sin(−(5*π)/4)

Solution

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

sin(−(5*π)/4)=−sin((5*π)/4)

2. Determine the reference angle for (5*π)/4 by identifying its position in the third quadrant.

(5*π)/4=π+π/4

3. Evaluate the sine in the third quadrant, where sine is negative, using the reference angle π/4

sin((5*π)/4)=−sin(π/4)

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

sin((5*π)/4)=−√(,2)/2

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

−(−√(,2)/2)=√(,2)/2

Final Answer

sin(−(5*π)/4)=√(,2)/2

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