Answer:
Explanation:
If cos(a) = 2/5 then sin(a) = ±√(1 - cos²(a)) = ±√(1 - 4/25) = ±3/5 (since a is in the fourth quadrant, sin(a) is negative)
To solve sin(a + π/3), we use the formula:
sin(a + π/3) = sin(a)cos(π/3) + cos(a)sin(π/3)
= (3/5)(√3/2) + (2/5)(1/2) = (3√3 + 2)/10
Therefore, the value of sin(a + π/3) is (3√3 + 2)/10.