Find the Exact Value sin(225 degrees )

Problem

sin(225)

Solution

1. Identify the reference angle by determining how far 225 is from the horizontal axis (180.

(θ_ref)=225−180=45

2. Determine the quadrant in which the angle 225 lies. Since 180<225<270 the angle is in Quadrant III.

3. Determine the sign of the sine function in Quadrant III. In this quadrant, the ycoordinates are negative, so sin(θ) is negative.

sin(225)=−sin(45)

4. Substitute the known exact value for sin(45) which is √(,2)/2

sin(225)=−√(,2)/2

Final Answer

sin(225)=−√(,2)/2

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