Find the Exact Value sin(-225)

Problem

sin(−225^∘)

Solution

1. Use the odd function property of the sine function, which states that sin(−θ)=−sin(θ)

sin(−225^∘)=−sin(225^∘)

2. Find the reference angle for 225^∘ Since 225^∘ is in the third quadrant, subtract 180^∘ from the angle.

Reference Angle=225^∘−180^∘=45^∘

3. Determine the sign of the sine function in the third quadrant. In the third quadrant, sine is negative.

sin(225^∘)=−sin(45^∘)

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

sin(225^∘)=−√(,2)/2

5. Apply the negative sign from the first step to find the final value.

−sin(225^∘)=−(−√(,2)/2)

sin(−225^∘)=√(,2)/2

Final Answer

sin(−225^∘)=√(,2)/2

Want more problems? Check here!