Find the Value Using the Unit Circle sin(225)

Problem

sin(225)

Solution

1. Identify the position of the angle 225 on the unit circle. Since 180<225<270 the angle lies in Quadrant III.

2. Calculate the reference angle by subtracting 180 from the given angle.

(θ_ref)=225−180=45

3. Determine the sign of the sine function in Quadrant III. In this quadrant, both x and y coordinates are negative, so sin(θ)<0

4. Apply the known value for the reference angle sin(45)=√(,2)/2 and attach the negative sign.

sin(225)=−sin(45)

Final Answer

sin(225)=−√(,2)/2

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