Evaluate sin(225 degrees )

Problem

sin(225^∘)

Solution

1. Identify the quadrant of the angle. Since 180^∘<225^∘<270^∘ the angle 225^∘ lies in the third quadrant.

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

3. Calculate the reference angle. The reference angle (θ_ref) is found by subtracting 180^∘ from the given angle.

(θ_ref)=225^∘−180^∘

(θ_ref)=45^∘

4. Apply the reference angle property. The value of sin(225^∘) is equal to −sin(45^∘)

5. Substitute the known value for sin(45^∘)

sin(45^∘)=√(,2)/2

sin(225^∘)=−√(,2)/2

Final Answer

sin(225^∘)=−√(,2)/2

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