Find the Exact Value cos(45 degrees )

Problem

cos(45)

Solution

1. Identify the angle in the context of the unit circle or a special right triangle. The angle 45 corresponds to an isosceles right triangle (45−45−90.

2. Recall the side ratios for a 45−45−90 triangle, where the legs are 1 and the hypotenuse is √(,2)

3. Apply the definition of the cosine function, which is the ratio of the adjacent side to the hypotenuse.

cos(45)=1/√(,2)

4. Rationalize the denominator by multiplying the numerator and the denominator by √(,2)

1/√(,2)⋅√(,2)/√(,2)=√(,2)/2

Final Answer

cos(45)=√(,2)/2

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