Find the Value Using the Unit Circle cos(45 degrees )

Problem

cos(45^∘)

Solution

1. Identify the angle on the unit circle. The angle 45^∘ is located in the first quadrant.

2. Determine the coordinates (x,y) for the given angle. On the unit circle, an angle of 45^∘ corresponds to the point (√(,2)/2,√(,2)/2)

3. Apply the definition of the cosine function. On the unit circle, cos(θ) is equal to the xcoordinate of the point.

4. Extract the xvalue from the coordinates.

Final Answer

cos(45^∘)=√(,2)/2

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