Find the Exact Value cos(990)

Problem

cos(990)

Solution

1. Find the coterminal angle by subtracting multiples of 360 until the angle is within the range [0,360)

990−2⋅360=990−720

990−720=270

2. Identify the position of the coterminal angle on the unit circle. The angle 270 is located on the negative y-axis.

3. Determine the coordinates at 270 On the unit circle, the coordinates are (0,−1)

4. Apply the definition of the cosine function, which corresponds to the x-coordinate of the point on the unit circle.

cos(270)=0

Final Answer

cos(990)=0

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