Cos45

To find the value of cos(45), you can use the unit circle or a calculator. The unit circle is a circle with a radius of 1, centered at the origin of a coordinate plane.

Alternatively, you can use the trigonometric identity cosine of the sum of angles:
cos(a + b) = cos(a)cos(b) - sin(a)sin(b)

In this case, think of 45 as the sum of two angles, 30 and 15.

cos(45) = cos(30 + 15)
Using the cosine of the sum of angles identity:
cos(30 + 15) = cos(30)cos(15) - sin(30)sin(15)

You can use calculator functions to calculate the values of cos(30) and cos(15), or you can use trigonometric values from a table.

Once you have the values of cos(30) and cos(15), you can substitute them into the formula to find cos(45):
cos(45) = cos(30)cos(15) - sin(30)sin(15)

Using a calculator or trigonometric values, you can plug in the values and solve for cos(45). The answer is approximately 0.7071.