Find the Exact Value cos(255)

Problem

cos(255)

Solution

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

cos(255)=cos(210+45)

2. Apply the cosine sum formula, which states cos(A+B)=cos(A)*cos(B)−sin(A)*sin(B)

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

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

cos(210)=−√(,3)/2

sin(210)=−1/2

cos(45)=√(,2)/2

sin(45)=√(,2)/2

4. Multiply the terms together.

(−√(,3)/2)*(√(,2)/2)−(−1/2)*(√(,2)/2)

−√(,6)/4+√(,2)/4

5. Simplify the expression by combining the fractions over a common denominator.

(√(,2)−√(,6))/4

Final Answer

cos(255)=(√(,2)−√(,6))/4

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