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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