Find the Exact Value sin(-(9pi)/4)

Problem

sin(−(9*π)/4)

Solution

1. Identify the angle as a negative value and use the odd-function property of sine, which states sin(−x)=−sin(x)

sin(−(9*π)/4)=−sin((9*π)/4)

2. Find a coterminal angle within the interval [0,2*π] by subtracting 2*π (which is (8*π)/4 from the argument.

(9*π)/4−(8*π)/4=π/4

3. Substitute the coterminal angle back into the expression.

−sin((9*π)/4)=−sin(π/4)

4. Evaluate the sine of the reference angle π/4 using the unit circle or special right triangles.

sin(π/4)=√(,2)/2

5. Apply the negative sign from the first step to find the final value.

−√(,2)/2

Final Answer

sin(−(9*π)/4)=−√(,2)/2

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