Find the Exact Value sin(-(5pi)/2)

Problem

sin(−(5*π)/2)

Solution

1. Identify the angle and its periodicity. The sine function has a period of 2*π which is equivalent to (4*π)/2

2. Add the period to the angle to find a coterminal angle within the standard range.

θ=−(5*π)/2+2*π

θ=−(5*π)/2+(4*π)/2

θ=−π/2

3. Add another period if necessary to reach a positive coterminal angle.

θ=−π/2+(4*π)/2

θ=(3*π)/2

4. Evaluate the sine function at the coterminal angle (3*π)/2 using the unit circle. At this position, the coordinates are (0,−1)

sin((3*π)/2)=−1

Final Answer

sin(−(5*π)/2)=−1

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