Question

find the period in degrees of $f(x)=\frac{1}{2}cos(\frac{x}{3})$ 1080 degrees 180 degrees 120 degrees 720 degrees 14 multiple choice 1 point find the period in degrees of $f(x)=\frac{1}{2}sin(3x)$ 120 degrees 180 degrees 1080 degrees 720 degrees

Explanation:

Step1: Recall the formula for the period of a trigonometric function

The period of \(y = A\sin(Bx)\) or \(y=A\cos(Bx)\) (in degrees) is given by \(T=\frac{360^{\circ}}{|B|}\).

Step2: Identify the value of \(B\) for \(f(x)=\frac{1}{2}\sin(3x)\)

For the function \(f(x)=\frac{1}{2}\sin(3x)\), we have \(B = 3\).

Step3: Calculate the period

Substitute \(B = 3\) into the period formula \(T=\frac{360^{\circ}}{|B|}\). So \(T=\frac{360^{\circ}}{3}=120^{\circ}\).

Answer:

120 degrees