Question

Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar.Function g is a transformation of the parent sine function, /(E)= sin(e)g(=) = join(2= - 5) + 1

Answer 1

GIVEN;

We are given a trig function as shown below;

$g(x)=\frac{1}{3}sin(2x-5)+1$

Required;

To determine the phase shift of this trig function.

Step-by-step solution;

For the function;

$\begin{gathered} f(x)=A\cdot g(Bx-C)+D \\ \\ Where\text{ }g(x)\text{ }is\text{ }one\text{ }of\text{ }the\text{ }basic\text{ }trig\text{ }functions; \\ \\ \frac{C}{B}\text{ }is\text{ }phase\text{ }shift \\ \\ D\text{ }is\text{ }vertical\text{ }shift \end{gathered}$

Therefore,

$\begin{gathered} g(Bx-C)=sin(2x-5) \\ \\ B=2,C=5,D=1 \end{gathered}$

Hence, phase shift is;

$Phase\text{ }shift=\frac{C}{B}=\frac{5}{2}$

ANSWER:

$\frac{5}{2}$