Subjects trigonometry

Sine Function 97Eec7

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1. **Stating the problem:** We are given the function $y = 2 \sin x$ and need to analyze its graph characteristics and verify the truth of several statements about amplitude, maximum value, x-intercepts, minimum value, and period. 2. **Formula and rules:** The general sine function is $y = A \sin(Bx + C) + D$ where: - Amplitude = $|A|$ - Period = $\frac{2\pi}{|B|}$ - Maximum value = $D + |A|$ - Minimum value = $D - |A|$ - The sine function crosses the x-axis at multiples of $\pi$ when $C=0$ and $D=0$. 3. **Apply to $y = 2 \sin x$:** - Amplitude $= |2| = 2$ - Period $= \frac{2\pi}{1} = 2\pi$ - Maximum value $= 0 + 2 = 2$ - Minimum value $= 0 - 2 = -2$ - X-intercepts occur at $x = k\pi$ for integer $k$, so at $0, \pm \pi, \pm 2\pi, ...$ 4. **Check statements:** - "Amplitudo sama dengan 2" (Amplitude is 2): True - "Nilai maksimum 1" (Maximum value is 1): False, max is 2 - "Grafik memotong di titik (0,0)" (Graph crosses at (0,0)): True, since $\sin 0 = 0$ - "Memiliki nilai minimum -2" (Has minimum value -2): True - "Memiliki periode 2\pi" (Has period $2\pi$): True **Final answer:** - Amplitude = 2 (True) - Maximum = 1 (False, actual 2) - Crosses (0,0) (True) - Minimum = -2 (True) - Period = $2\pi$ (True)