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

Problem

sin((9*π)/4)

Solution

1. Identify the angle and determine its position on the unit circle. The angle (9*π)/4 is greater than 2*π

2. Find the coterminal angle by subtracting 2*π (one full rotation) from the given angle.

(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 This is a standard angle in the first quadrant where the coordinates are (√(,2)/2,√(,2)/2)

sin((9*π)/4)=sin(π/4)

4. Determine the exact value using the unit circle or special right triangles.

sin(π/4)=√(,2)/2

Final Answer

sin((9*π)/4)=√(,2)/2

Want more problems? Check here!