Find the Exact Value sin(-135 degrees )

Problem

sin(−135)

Solution

1. Identify the reference angle by adding 360 to find a coterminal angle within the standard range [0,360]

−135+360=225

2. Determine the quadrant of the angle. Since 225 is between 180 and 270 the angle lies in Quadrant III.

3. Calculate the reference angle (θ_r*e*ƒ) for an angle in Quadrant III using the formula (θ_r*e*ƒ)=θ−180

(θ_r*e*ƒ)=225−180=45

4. Apply the sign of the sine function in Quadrant III. In Quadrant III, the sine value is negative.

sin(−135)=−sin(45)

5. Substitute the known exact value for sin(45) which is √(,2)/2

sin(−135)=−√(,2)/2

Final Answer

sin(−135)=−√(,2)/2

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