Evaluate sin(255)

Problem

sin(255)

Solution

1. Rewrite the angle as a sum of two special angles from the unit circle.

sin(255)=sin(210+45)

2. Apply the sine addition formula, which states sin(A+B)=sin(A)*cos(B)+cos(A)*sin(B)

sin(210+45)=sin(210)*cos(45)+cos(210)*sin(45)

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

sin(210)=−1/2

cos(210)=−√(,3)/2

sin(45)=√(,2)/2

cos(45)=√(,2)/2

4. Substitute these values back into the addition formula.

sin(255)=(−1/2)*(√(,2)/2)+(−√(,3)/2)*(√(,2)/2)

5. Simplify the expression by performing the multiplication and combining the fractions.

sin(255)=−√(,2)/4−√(,6)/4

sin(255)=(−√(,2)−√(,6))/4

Final Answer

sin(255)=−(√(,2)+√(,6))/4

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