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

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