Find the Exact Value sin(-315 degrees )

Problem

sin(−315^∘)

Solution

1. Find a coterminal angle by adding 360^∘ to the given negative angle to find its equivalent position within the first rotation.

θ=−315^∘+360^∘=45^∘

2. Identify the reference angle for 45^∘ which is already in the first quadrant.

(θ_ref)=45^∘

3. Determine the sign of the sine function in the first quadrant. Since 45^∘ is in Quadrant I, the sine value is positive.

sin(−315^∘)=sin(45^∘)

4. Evaluate the exact value using the unit circle or special right triangles.

sin(45^∘)=√(,2)/2

Final Answer

sin(−315^∘)=√(,2)/2

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