Find the Exact Value sin(585)

Problem

sin(585)

Solution

1. Find the coterminal angle by subtracting 360 from the given angle to bring it within the range of 0 to 360

585−360=225

2. Determine the quadrant of the angle 225 Since 180<225<270 the angle lies in Quadrant III.

3. Calculate the reference angle for an angle in Quadrant III using the formula (θ_ref)=θ−180

225−180=45

4. Determine the sign of the sine function in Quadrant III. In this quadrant, sine is negative.

sin(225)=−sin(45)

5. Substitute the known value for sin(45) which is √(,2)/2

−sin(45)=−√(,2)/2

Final Answer

sin(585)=−√(,2)/2

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