Final answer:
The cook should use 3/8 of a cup of sugar.
Step-by-step explanation:
To find how much sugar the cook should use, we need to determine how much sugar is needed for 1/2 of the recipe. The original recipe calls for 3/4 of a cup of sugar, so 1/2 of the recipe would require half of 3/4 of a cup.
To calculate this, we can multiply 3/4 by 1/2:
3/4 * 1/2 = (3*1)/(4*2) = 3/8
Therefore, the cook should use 3/8 of a cup of sugar.