Find the Exact Value cos(165 degrees )

Problem

cos(165)

Solution

1. Identify the angle 165 as a sum of two special angles from the unit circle, such as 120 and 45

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

3. Substitute the values A=120 and B=45 into the formula.

cos(165)=cos(120+45)

cos(165)=cos(120)*cos(45)−sin(120)*sin(45)

4. Evaluate the trigonometric functions for the special angles.

cos(120)=−1/2

sin(120)=√(,3)/2

cos(45)=√(,2)/2

sin(45)=√(,2)/2

5. Multiply the terms together.

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!