Evaluate sin(-45 degrees )

Problem

sin(−45^∘)

Solution

1. Identify the property of the sine function for negative angles. Since sine is an odd function, sin(−θ)=−sin(θ)

2. Apply the property to the given expression.

sin(−45^∘)=−sin(45^∘)

3. Recall the exact value of sin(45^∘) from the unit circle or a special right triangle (45^∘−45^∘−90^∘.

sin(45^∘)=√(,2)/2

4. Substitute the value back into the expression.

−sin(45^∘)=−√(,2)/2

Final Answer

sin(−45^∘)=−√(,2)/2

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