Find the Exact Value sin(225)

Problem

sin(225^∘)

Solution

1. Identify the angle's position on the unit circle. The angle 225^∘ is located in the third quadrant because 180^∘<225^∘<270^∘

2. Calculate the reference angle (θ_r*e*ƒ) by subtracting 180^∘ from the given angle.

(θ_r*e*ƒ)=225^∘−180^∘=45^∘

3. Determine the sign of the sine function in the third quadrant. In the third quadrant, the ycoordinates are negative, so sin(225^∘) must be negative.

4. Apply the reference angle value. The sine of 45^∘ is √(,2)/2

sin(225^∘)=−sin(45^∘)

5. Substitute the known value to find the final result.

sin(225^∘)=−√(,2)/2

Final Answer

sin(225^∘)=−√(,2)/2

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