Find the Exact Value cos(840)

Problem

cos(840)

Solution

1. Find the coterminal angle by subtracting multiples of 360 until the angle is between 0 and 360

840−2*(360)=840−720

840−720=120

2. Identify the quadrant for 120 Since 90<120<180 the angle lies in Quadrant II.

3. Determine the sign of the cosine function in Quadrant II. In this quadrant, cosine is negative.

4. Find the reference angle for 120 by subtracting it from 180

180−120=60

5. Evaluate the cosine of the reference angle using known trigonometric values.

cos(60)=1/2

6. Apply the sign from step 3 to the value found in step 5.

cos(120)=−1/2

Final Answer

cos(840)=−1/2

Want more problems? Check here!