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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