Find the Exact Value cos(45)

Problem

cos(45)

Solution

1. Identify the angle on the unit circle. The angle 45 is a standard angle in the first quadrant.

2. Recall the coordinates of the terminal point for 45 on the unit circle, which are (√(,2)/2,√(,2)/2)

3. Apply the definition of the cosine function. For any point (x,y) on the unit circle, cos(θ)=x

4. Determine the value by selecting the x-coordinate of the point.

Final Answer

cos(45)=√(,2)/2

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