Find the exactly value of sin2(alpha) if cos(alpha) = 4/5 (alpha in Quadrant I)

To find the exact value of sin²(α), we can use the Pythagorean identity: sin²(α) + cos²(α) = 1. Since we are given that cos(α) = 4/5, we can substitute this value into the equation and solve for sin²(α).

sin²(α) + (4/5)² = 1
sin²(α) + 16/25 = 1
sin²(α) = 1 - 16/25
sin²(α) = 25/25 - 16/25
sin²(α) = 9/25

Therefore, the exact value of sin²(α) is 9/25.

Note: Since we are in Quadrant I, both sin(α) and cos(α) are positive, which is why we take the positive square root when solving for sin(α).