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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