Find the Exact Value sin(225 degrees )

Problem

sin(225^∘)

Solution

1. Identify the reference angle by determining how far 225^∘ is from the horizontal axis (180^∘.

(θ_ref)=225^∘−180^∘=45^∘

2. Determine the quadrant in which the angle 225^∘ lies. Since 180^∘<225^∘<270^∘ the angle is in Quadrant III.

3. Determine the sign of the sine function in Quadrant III. In this quadrant, the ycoordinates are negative, so sin(θ) is negative.

sin(225^∘)=−sin(45^∘)

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

sin(225^∘)=−√(,2)/2

Final Answer

sin(225^∘)=−√(,2)/2

Want more problems? Check here!