What is the exact value of cos 45º ?
enter your answer, as a simplified fraction, in the box.

(√2)/2

Step-by-step explanation:

A right triangle with one acute angle equal to 45° will also have the other acute angle equal to 45°. The angles being equal means the legs will be equal. If we assign each leg the length 1, then the Pythagorean theorem tells us the hypotenuse is length ...

√(1^2 +1^2) = √2

The cosine of the acute angle is the ratio of the nearest leg length (1) to the hypotenuse length (√2), so the exact value of the cosine is ...

cos(45°) = 1/√2 = (√2)/2

(√2)/2 is the fraction with the denominator "rationalized". Sometimes, that is the preferred presentation of this number.

triangle and cube

step-by-step explanation: