taiwan-gsat 2025 Q19

taiwan-gsat · Other · gsat__math-b 6 marks Trig Graphs & Exact Values
On a certain day at a certain location, the duration of daylight (from sunrise to sunset) is exactly 12 hours. The UVI value at that location $x$ hours after sunrise ($0 \leq x \leq 12$) can be expressed by the function $f ( x ) = a \sin ( b x )$ , where $a , b > 0$ . Assume that the UVI value is positive during daylight and 0 during non-daylight hours (i.e., $f ( 0 ) = f ( 12 ) = 0$), and the UVI value 2 hours after sunrise on that day is 4. Find the values of $a$ and $b$.
On a certain day at a certain location, the duration of daylight (from sunrise to sunset) is exactly 12 hours. The UVI value at that location $x$ hours after sunrise ($0 \leq x \leq 12$) can be expressed by the function $f ( x ) = a \sin ( b x )$ , where $a , b > 0$ . Assume that the UVI value is positive during daylight and 0 during non-daylight hours (i.e., $f ( 0 ) = f ( 12 ) = 0$), and the UVI value 2 hours after sunrise on that day is 4. Find the values of $a$ and $b$.