A particle moves along a curve described by y=3sin(1over2 x+60degrees).state amplitude,phase angle and period

The equation of the particle's motion is given by:

\[
y = 3 \sin\left(\frac{1}{2}x + 60^\circ\right)
\]

Let's break this down step by step:

### 1. **Amplitude:**
The amplitude of a sine function, \( y = A \sin(Bx + C) \), is given by the coefficient \( A \), which represents the maximum displacement from the centerline.

Here, the amplitude is \( 3 \). Therefore:
\[
\text{Amplitude} = 3
\]

### 2. **Phase Angle:**
The phase angle in a sine function is given by the constant term added inside the sine function, \( C \), when written in the form \( \sin(Bx + C) \). Here, the phase angle is \( 60^\circ \).

Thus:
\[
\text{Phase angle} = 60^\circ
\]

### 3. **Period:**
The period of a sine function is determined by the coefficient \( B \) in the argument \( \sin(Bx) \). The formula for the period is:

\[
\text{Period} = \frac{360^\circ}{B}
\]

In this case, \( B = \frac{1}{2} \), so the period is:

\[
\text{Period} = \frac{360^\circ}{\frac{1}{2}} = 720^\circ
\]

### Summary:
- **Amplitude**: 3
- **Phase angle**: \( 60^\circ \)
- **Period**: \( 720^\circ \)

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A particle moves along a curve described by y=3sin(1/2 x + 60 degrees). State amplitude, phase angle, and period.

Learn how to find the amplitude, phase angle, and period for the trigonometric function y = 3sin(1/2 x + 60°). This problem covers key trigonometric concepts, including the sine function's properties and periodicity, suitable for high school students in Grades 10-12.

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