Find the Exact Value sin((9pi)/2)

Problem

sin((9*π)/2)

Solution

1. Identify the angle in the sine function, which is (9*π)/2

2. Determine the coterminal angle within the standard interval [0,2*π) by subtracting multiples of 2*π

3. Calculate the subtraction: (9*π)/2−4*π=(9*π)/2−(8*π)/2=π/2

4. Evaluate the sine of the coterminal angle π/2 using the unit circle.

5. Recall that sin(π/2)=1

Final Answer

sin((9*π)/2)=1

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