Find the Exact Value cos(690)

Problem

cos(690^∘)

Solution

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

690^∘−360^∘=330^∘

2. Determine the quadrant for 330^∘ Since 270^∘<330^∘<360^∘ the angle lies in Quadrant IV.

3. Find the reference angle for an angle in Quadrant IV by subtracting the angle from 360^∘

360^∘−330^∘=30^∘

4. Determine the sign of the cosine function in Quadrant IV. Cosine is positive in the fourth quadrant.

cos(690^∘)=cos(30^∘)

5. Evaluate the cosine of the reference angle using the unit circle or special right triangles.

cos(30^∘)=√(,3)/2

Final Answer

cos(690^∘)=√(,3)/2

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