Find the Exact Value sin((25pi)/2)

Problem

sin((25*π)/2)

Solution

1. Identify the period of the sine function, which is 2*π

2. Divide the coefficient 25/2 by 2 to determine how many full rotations are contained in the angle.

25/2=12.5

3. Subtract the nearest even multiple of π to find the coterminal angle within the interval [0,2*π)

(25*π)/2−12*π=(25*π)/2−(24*π)/2

(25*π)/2−(24*π)/2=π/2

4. Evaluate the sine of the coterminal angle.

sin(π/2)=1

Final Answer

sin((25*π)/2)=1

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