Questions: Question 10 For the equation, identify the amplitude, period, and phase shift and sketch (at least) one complete cycle of the graph. y = 1/2 sin(3x + π/2) Amplitude: Period: Phase Shift: Clear All Draw: M

Solution Steps

The given equation is \( y = \frac{1}{2} \sin \left( 3x + \frac{\pi}{2} \right) \).

The amplitude of a sine function \( y = A \sin(Bx + C) \) is given by the absolute value of \( A \). Here, \( A = \frac{1}{2} \).

Amplitude: \[ \text{Amplitude} = \left| \frac{1}{2} \right| = \frac{1}{2} \]

The period of a sine function \( y = A \sin(Bx + C) \) is given by \( \frac{2\pi}{B} \). Here, \( B = 3 \).

Period: \[ \text{Period} = \frac{2\pi}{3} \]

The phase shift of a sine function \( y = A \sin(Bx + C) \) is given by \( -\frac{C}{B} \). Here, \( C = \frac{\pi}{2} \) and \( B = 3 \).

Phase Shift: \[ \text{Phase Shift} = -\frac{\frac{\pi}{2}}{3} = -\frac{\pi}{6} \]

Final Answer