Find the Exact Value sin(1305)

Problem

sin(1305)

Solution

1. Find the coterminal angle by dividing 1305 by 360 to determine how many full rotations are in the angle.

1305÷360=3.625

2. Subtract the full rotations from the original angle to find an angle between 0 and 360

1305−3*(360)=1305−1080

1305−1080=225

3. Identify the quadrant for 225 Since 180<225<270 the angle lies in Quadrant III, where the sine function is negative.

sin(1305)=sin(225)

4. Determine the reference angle by subtracting 180 from the angle.

(θ_ref)=225−180

(θ_ref)=45

5. Apply the sine value for the reference angle and attach the appropriate sign for Quadrant III.

sin(225)=−sin(45)

sin(45)=√(,2)/2

Final Answer

sin(1305)=−√(,2)/2

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