Find the Exact Value sin(-300)

Problem

sin(−300^∘)

Solution

1. Identify the reference angle by adding 360^∘ to the negative angle to find its coterminal equivalent within the range [0^∘,360^∘]

−300^∘+360^∘=60^∘

2. Determine the quadrant of the angle. Since 60^∘ is between 0^∘ and 90^∘ the angle lies in Quadrant I.

3. Apply the property that the sine function is positive in Quadrant I.

sin(−300^∘)=sin(60^∘)

4. Evaluate the exact value of the sine of 60^∘ using the unit circle or special right triangles.

sin(60^∘)=√(,3)/2

Final Answer

sin(−300^∘)=√(,3)/2

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