Simplify sin(225)

Problem

sin(225^∘)

Solution

1. Identify the angle in the coordinate plane. The angle 225^∘ is in the third quadrant because 180^∘<225^∘<270^∘

2. Determine the reference angle. For an angle θ in the third quadrant, the reference angle θ^′ is calculated as θ−180^∘

θ^′=225^∘−180^∘=45^∘

3. Determine the sign of the sine function. In the third quadrant, the sine of an angle is negative.

sin(225^∘)=−sin(45^∘)

4. Evaluate the sine of the reference angle using known trigonometric values.

sin(45^∘)=√(,2)/2

5. Combine the sign and the value to find the final result.

sin(225^∘)=−√(,2)/2

Final Answer

sin(225^∘)=−√(,2)/2

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