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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