Find the Exact Value sin(315)

Problem

sin(315)

Solution

1. Identify the reference angle by finding the difference between 315 and the nearest x-axis angle, which is 360

360−315=45

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

3. Determine the sign of the sine function in Quadrant IV. In this quadrant, the y-coordinates are negative, so sin(315) must be 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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