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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