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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