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

Problem

sin((9*π)/4)

Solution

1. Identify the angle and determine if it is greater than one full revolution of 2*π radians.

2. Find the coterminal angle by subtracting 2*π from the given angle to bring it within the interval [0,2*π)

(9*π)/4−2*π=(9*π)/4−(8*π)/4

(9*π)/4−(8*π)/4=π/4

3. Evaluate the sine function at the coterminal angle π/4

sin((9*π)/4)=sin(π/4)

4. Use the unit circle or special right triangles to find the exact value of sin(π/4)

sin(π/4)=√(,2)/2

Final Answer

sin((9*π)/4)=√(,2)/2

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