Write the Word or Phrase That Best Completes Each Statement $f ( x ) = \frac { 4 } { \pi } \left[ \sin ( \pi x ) + \frac { 1 } { 3 } \right.$

Essay

Write the word or phrase that best completes each statement or answers the question.
Solve the problem.
-A square wave is built up from sinusoidal curves of varying periods and amplitudes.
Graph the following function, which can be used to approximate the square wave. $f ( x ) = \frac { 4 } { \pi } \left[ \sin ( \pi x ) + \frac { 1 } { 3 } \right.$
$0 \leq x \leq 4$


A better approximation to the square wave is given by $$f ( x ) = \frac { 4 } { \pi } \left[ \sin ( \pi x ) + \frac { 1 } { 3 } \sin ( 3 \pi x ) + \frac { 1 } { 5 } \sin ( 5 \pi x ) \right] 0 \leq x \leq 4$$


Graph this function and compare the result to the previous graph. Adding another term will improve the approximation
even more. Write this new function with four terms.