Final answer:
The value of the expression sin(2θ) where θ = π/3 is (√3/2).
Step-by-step explanation:
To find the value of the expression sin(2θ) where θ = π/3, we can use the double-angle identity for sine. The double-angle identity states that sin(2θ) = 2sinθcosθ.
First, we substitute θ = π/3 into the double-angle identity: sin(2(π/3)) = 2sin(π/3)cos(π/3).
Next, we simplify the expression: sin(2(π/3)) = 2(√3/2)(1/2) = (√3/2).
Therefore, the value of the expression sin(2θ) where θ = π/3 is (√3/2).
To find the value of the expression sin(2θ) where θ = π/3, first recall the double angle formula for sine, which is sin(2a) = 2sin(a)cos(a). Using this formula with θ = π/3, we can write sin(2θ) = sin(2(π/3)) = 2sin(π/3)cos(π/3). The values of sin(π/3) and cos(π/3) are √3/2 and 1/2, respectively. By substituting these values into the equation, we get sin(2θ) = 2(√3/2)(1/2) = √3/2.