Find the Exact Value cos(-165)

Problem

cos(−165)

Solution

1. Apply the even-odd identity for the cosine function, which states cos(−θ)=cos(θ)

cos(−165)=cos(165)

2. Rewrite the angle as a sum or difference of special angles from the unit circle.

165=120+45

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

cos(120+45)=cos(120)*cos(45)−sin(120)*sin(45)

4. Substitute the exact values for the sine and cosine of the special angles.

cos(120)=−1/2

cos(45)=√(,2)/2

sin(120)=√(,3)/2

sin(45)=√(,2)/2

5. Multiply the terms to simplify the expression.

cos(165)=(−1/2)*(√(,2)/2)−(√(,3)/2)*(√(,2)/2)

cos(165)=−√(,2)/4−√(,6)/4

6. Combine the fractions over a common denominator.

cos(165)=(−√(,2)−√(,6))/4

Final Answer

cos(−165)=(−√(,2)−√(,6))/4

Want more problems? Check here!