Find the Exact Value cos(-150 degrees )

Problem

cos(−150^∘)

Solution

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

cos(−150^∘)=cos(150^∘)

2. Find the reference angle for 150^∘ Since 150^∘ is in the second quadrant, the reference angle is 180^∘−150^∘=30^∘

(θ_ref)=30^∘

3. Determine the sign of the cosine function in the second quadrant. Since cosine represents the x-coordinate on the unit circle, it is negative in the second quadrant.

cos(150^∘)=−cos(30^∘)

4. Substitute the known value for cos(30^∘) which is √(,3)/2

cos(150^∘)=−√(,3)/2

Final Answer

cos(−150^∘)=−√(,3)/2

Want more problems? Check here!