What is the exact value of $\cos 45°$?

• A. $\frac{1}{\sqrt{2}}$
• B. $\frac{1}{2}$
• C. $\frac{\sqrt{2}}{2}$
• D. $\sqrt{3}$

Answer: (C)

Verified step by step guidance

1. Recall that the cosine of 45 degrees is a well-known special angle value in trigonometry.
2. Use the fact that 45 degrees corresponds to \( \frac{\pi}{4} \) radians, and the cosine of this angle can be derived from an isosceles right triangle where the two legs are equal.
3. In such a triangle, if each leg has length 1, then the hypotenuse has length \( \sqrt{2} \) by the Pythagorean theorem.
4. The cosine of 45 degrees is the ratio of the adjacent side to the hypotenuse, which is \( \frac{1}{\sqrt{2}} \).
5. To express this in a simplified exact form, rationalize the denominator by multiplying numerator and denominator by \( \sqrt{2} \), resulting in \( \frac{\sqrt{2}}{2} \).