Simplify sin(315)

Problem

sin(315)

Solution

1. Identify the reference angle by finding the difference between 315 and 360

Reference Angle=360−315=45

2. Determine the quadrant in which 315 lies. Since 270<315<360 the angle is in the fourth quadrant.

3. Apply the sign rule for the sine function. In the fourth quadrant, the sine of an angle is negative.

sin(315)=−sin(45)

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

sin(315)=−√(,2)/2

Final Answer

sin(315)=−√(,2)/2

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