Find the Exact Value sin(300)

Problem

sin(300^∘)

Solution

1. Identify the reference angle by finding the distance between 300^∘ and the nearest x-axis value, which is 360^∘

360^∘−300^∘=60^∘

2. Determine the quadrant of the angle. Since 300^∘ is between 270^∘ and 360^∘ it lies in Quadrant IV.

3. Determine the sign of the sine function in Quadrant IV. In this quadrant, the y-coordinates are negative, so the sine value is negative.

sin(300^∘)=−sin(60^∘)

4. Apply the known value for the sine of 60^∘

sin(60^∘)=√(,3)/2

5. Combine the sign and the value to find the final result.

sin(300^∘)=−√(,3)/2

Final Answer

sin(300^∘)=−√(,3)/2

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