Apair of functions f and g are said to be orthogonal on the interval [a, b] if b f(x g(x dx a = 0. a family of functions is said to be orthogonal on [a, b] if each distinct pair of functions f? g in the family is orthogonal on [a, b]. in this problem, you will show that the family of trigonometric functions sin(x, cos(x, sin(2x, cos(2x, sin(nx, cos(nx, is orthogonal on the interval [0, 2? ].

options a,b,c are the right answer.

step-by-step explanation:

a linear parent function is always represented as y = x

if we write this function in the form of y=mx+c

⇒

or  

now if we plot a graph we will find these characteristics:

1) y intercept of the graph is zero so its a straight line passing through origin.

2) as we can see in both the forms of function written, values of x and y may be either positive or negative for the positive slope means points on the graph are either in first quadrant or in third one.

3) it's slope is one.