To calculate sin (π/6 - a) using the given information that cos a = 0.6 and a = 3π/2, we can follow these steps:
Step 1: Determine the value of sin a using the given cos a value. Since cos a = 0.6, we can use the Pythagorean identity sin^2 a + cos^2 a = 1 to find sin a.
sin^2 a = 1 - cos^2 a
sin^2 a = 1 - 0.6^2
sin^2 a = 1 - 0.36
sin^2 a = 0.64
sin a = ± √0.64
Since a is in the third quadrant (3π/2), sin a will be negative. Therefore, sin a = -0.8.
Step 2: Substitute the value of a into sin (π/6 - a) and simplify.
sin (π/6 - a) = sin π/6 * cos a - cos π/6 * sin a
sin (π/6 - a) = (1/2) * 0.6 - (√3/2) * (-0.8)
sin (π/6 - a) = 0.3 + 0.8√3
Therefore, sin (π/6 - a) = 0.3 + 0.8√3.