Question

multiple choice 1 point
find the period in degrees of ( f(x)=-4 sin (2 x) )
180 degrees
720 degrees
90 degrees
1440 degrees
12
multiple choice 1 point
find the period in degrees of ( f(x)=-2 cos (4 x) )
90 degrees
720 degrees
180 degrees
1440 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 \(\frac{360^{\circ}}{|B|}\).

Step2: For \(f(x)= - 4\sin(2x)\)

Here \(B = 2\). Using the formula \(\frac{360^{\circ}}{|B|}\), we substitute \(B = 2\) into the formula: \(\frac{360^{\circ}}{2}=180^{\circ}\).

Step3: For \(f(x)=-2\cos(4x)\)

Here \(B = 4\). Using the formula \(\frac{360^{\circ}}{|B|}\), we substitute \(B = 4\) into the formula: \(\frac{360^{\circ}}{4} = 90^{\circ}\).

Answer:

For \(f(x)=-4\sin(2x)\): 180 degrees.
For \(f(x)=-2\cos(4x)\): 90 degrees.