cos 45°
√2/ 2
cos 45° is equal to √2 / 2.
To explain this further, we first need to understand what cosine means. In a right-angled triangle, cosine is the ratio of the adjacent side to the hypotenuse. In other words, it is the length of the side next to the angle (which is 45° in this case) divided by the length of the longest side of the triangle.
Now, since we know that the angle is 45°, we can draw the right-angled triangle and label the sides. If we assume that the hypotenuse has a length of 1 (which is common), then we can find the adjacent side using the Pythagorean theorem.
a^2 + b^2 = c^2
where c is the hypotenuse, and a and b are the other two sides.
In this case, we have:
a^2 + b^2 = 1^2
a^2 + b^2 = 1
Since we know that the angle is 45°, we can also see that the two other angles in the triangle are also 45° each. Therefore, the triangle is an isosceles right-angled triangle, which means that a = b.
Substituting this into the equation above, we get:
a^2 + a^2 = 1
2a^2 = 1
a^2 = 1 / 2
a = √2 / 2
Therefore, cos 45° (which is the ratio of the adjacent side to the hypotenuse) is equal to √2 / 2.
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