cos15

cos15 refers to the cosine of 15 degrees, a trigonometric function value. The exact value can be derived using the angle subtraction formula for cosine. By expressing 15 degrees as 45 degrees minus 30 degrees, we apply cos(a-b) = cos(a)cos(b) + sin(a)sin(b). Substituting a=45° and b=30°, we get cos15° = cos(45°-30°) = cos45°cos30° + sin45°sin30°. Using known values, cos45° = sin45° = √2/2, cos30° = √3/2, and sin30° = 1/2, we calculate cos15° = (√6 + √2)/4. This is approximately 0.9659 in decimal form. The value of cos15° is useful in geometry problems involving regular dodecagons, as 15 degrees represents 1/24 of a full circle. It also appears in various trigonometric identities and equations involving angles that are multiples of 15 degrees.