Find the Exact Value cos(150 degrees )

Problem

cos(150^∘)

Solution

1. Identify the reference angle by finding the distance from the terminal side to the x-axis. Since 150^∘ is in the second quadrant, the reference angle is 180^∘−150^∘=30^∘

2. Determine the sign of the cosine function in the second quadrant. In the second quadrant, the x-coordinates are negative, so cos(150^∘) must be negative.

3. Apply the reference angle rule which states that cos(θ)=±cos((θ_ref)) In this case, cos(150^∘)=−cos(30^∘)

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

Final Answer

cos(150^∘)=−√(,3)/2

Want more problems? Check here!