Find the Third-Degree Fourier Polynomial For $f(t)=$ $\left\{\begin{array}{l}0 \\c\end{array}\right.$ $\begin{array}{c}-2 <\\0<\end{array}$

question 29

Multiple Choice

Find the third-degree Fourier polynomial for $f(t) =$$\left\{\begin{array}{l}0 \\c\end{array}\right.$$\begin{array}{c}-2 <\\0<\end{array}$$\begin{array}{l}x \leq 0 \\x \leq 2\end{array}$ , where c is a constant, by writing a new function, $g(x) =f(t)$ , with period $2 \pi$ .

• A) \(\frac{c}{2}-\frac{2 c}{\pi} \sin \left(\frac{\pi t}{2}\right)-\frac{2 c}{3 \pi} \sin \left(\frac{3 \pi t}{2}\right)\)
• B) \(\frac{c}{2}+\frac{2 c}{\pi} \sin \left(\frac{\pi t}{2}\right)+\frac{2 c}{3 \pi} \sin \left(\frac{3 \pi t}{2}\right)\)
• C) \(\frac{c}{2}+\frac{2 c}{\pi} \sin (t)+\frac{2 c}{3 \pi} \sin (3 t)\)
• D) \(\frac{c}{2}-\frac{2 c}{\pi} \sin (t)-\frac{2 c}{3 \pi} \sin (3 t)\)

---

Definitions:

Physical Attractiveness

The degree to which a person's physical traits are considered aesthetically pleasing or beautiful in a cultural context.

Socioeconomic Status

Refers to an individual's or family's economic and social position in relation to others, based on income, education, and occupation.

Parents' Divorce

The legal termination of a marriage by the parents of a child or children, often leading to changes in family structure and dynamics.

Autonomous Morality

A stage in moral development where individuals recognize that rules and laws are created for the welfare of the population and can judge actions by their intentions rather than just their consequences.