Find the exact value of sin π/12.
To find the exact value of sin(π/12), we can use the relationship between the angles of a unit circle and the trigonometric functions.
Step 1: Start with the known values of sin and cos for the angles π/6 (30 degrees) and π/4 (45 degrees).
sin(π/6) = 1/2
cos(π/6) = √3/2
sin(π/4) = √2/2
cos(π/4) = √2/2
Step 2: Use the double angle formula for sine to find sin(π/12).
sin(π/12) = 2 * sin(π/6) * cos(π/6) - sin²(π/6)
= 2 * (1/2) * (√3/2) - (1/2)²
= √3/2 - 1/4
= (2√3 - 1)/4
Therefore, the exact value of sin(π/12) is (2√3 - 1)/4.