Find the Exact Value sin(285)

Problem

sin(285)

Solution

1. Identify the angle as a sum or difference of special angles from the unit circle.

sin(285)=sin(240+45)

2. Apply the sum formula for sine, which is sin(A+B)=sin(A)*cos(B)+cos(A)*sin(B)

sin(240+45)=sin(240)*cos(45)+cos(240)*sin(45)

3. Substitute the exact values for the trigonometric functions of the special angles.

sin(240)=−√(,3)/2

cos(45)=√(,2)/2

cos(240)=−1/2

sin(45)=√(,2)/2

4. Multiply the terms together.

sin(285)=(−√(,3)/2)*(√(,2)/2)+(−1/2)*(√(,2)/2)

sin(285)=−√(,6)/4−√(,2)/4

5. Combine the fractions over a common denominator.

sin(285)=(−√(,6)−√(,2))/4

Final Answer

sin(285)=(−√(,6)−√(,2))/4

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