College Math Placement Practice Test

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What is the cosine of 45 degrees?

0
1/2
√2/2
√3/2

The correct answer is: √2/2

The cosine of 45 degrees is √2/2, which is derived from the properties of a right triangle. In a 45-degree right triangle, the two legs are of equal length. If we assume each leg has a length of 1, using the Pythagorean theorem, the hypotenuse calculates to √(1^2 + 1^2) = √2. The cosine function, which is defined as the ratio of the adjacent side to the hypotenuse, results in: cos(45°) = adjacent / hypotenuse = 1 / √2. To express this in a more standard form, we can rationalize the denominator: 1 / √2 * (√2/√2) = √2 / 2. This gives us the accurate value of cos(45°) as √2/2. This understanding is foundational in trigonometry, particularly when dealing with angles that correspond to special triangles.