Subjects trigonometry

Fish Catch Sine

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Fish Catch Sine


1. The problem involves analyzing the fish catch results of three boats represented by the function $f(x) = a \sin kx$ where $x$ is the direction in degrees and $f(x)$ is the catch in kuintal. 2. We are given specific catch values at certain directions for each boat and need to verify statements about these values. 3. To solve, we use the sine function properties and given data points to find or verify the catch amounts. 4. For example, for Putri Duyung at $6^\circ$, the catch is given as 2.0 kuintal, and at $15^\circ$ as 2.4 kuintal. 5. We check the difference or sum of catches between boats at given directions by subtracting or adding their respective $f(x)$ values. 6. For the first statement in question 2: "Selisih banyaknya ikan yang didapat jika kapal Putri Duyung dan Tunggal Jaya berlayar dengan arah 3^\circ adalah 6,2 kuintal." - If Putri Duyung's catch at $3^\circ$ is $f_1(3)$ and Tunggal Jaya's catch is $f_2(3)$, then difference $|f_1(3) - f_2(3)|$ should be 6.2 kuintal. 7. Similarly, verify other statements by calculating sums or differences using the given catch values. 8. Since exact functions $a$ and $k$ are not provided, we rely on the given data points to confirm the truth of each statement. Final answers for question 2 (Benar = True, Salah = False): - Selisih ikan Putri Duyung dan Tunggal Jaya di $3^\circ$: Salah (does not equal 6.2) - Jumlah ikan Putri Duyung dan Tunggal Jaya di $6^\circ$: Benar (equals 9.4) - Jumlah ikan Putri Duyung dan Tunggal Jaya di $9^\circ$: Benar (equals 9.2) - Selisih ikan Putri Duyung dan Samudera Indah di $15^\circ$: Salah (not 8) - Selisih ikan Tunggal Jaya dan Samudera Indah di $10^\circ$: Salah (not 5.5) Thus, the problem is about interpreting and verifying values from the sine function model of fish catch.