Final answer:
Using the double-angle formula for sine and the given cosine value, we calculate sin(2θ) to be -2√{21}/10, considering that θ is in the fourth quadrant where sine is negative.
Step-by-step explanation:
To find sin(2θ) given that cos(θ) = √{3/10} and θ is in the fourth quadrant, we can use the double-angle formula for sine, which is sin(2θ) = 2sin(θ)cos(θ). However, first we need to find sin(θ). Since θ is in the fourth quadrant, sin(θ) must be negative and we can use the Pythagorean identity sin²(θ) + cos²(θ) = 1 to find sin(θ).
cos²(θ) = (√{3/10})² = 3/10
sin²(θ) = 1 - cos²(θ) = 1 - 3/10 = 7/10
sin(θ) = -√{7/10}
Now, apply the double-angle formula:
sin(2θ) = 2sin(θ)cos(θ) = 2(-√{7/10})(√{3/10})
sin(2θ) = -2√{21}/10