Find the Exact Value sin(-45 degrees )

Problem

sin(−45^∘)

Solution

1. Apply the odd-even identity for the sine function, which states that sin(−θ)=−sin(θ)

sin(−45^∘)=−sin(45^∘)

2. Identify the exact value of sin(45^∘) using the unit circle or a special right triangle (45^∘−45^∘−90^∘.

sin(45^∘)=√(,2)/2

3. Substitute the value back into the expression to find the final result.

−sin(45^∘)=−√(,2)/2

Final Answer

sin(−45^∘)=−√(,2)/2

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