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

Want more problems? Check here!