A person starts at 12 0 and walks t units along the perimete

A person starts at (1/2, 0) and walks t units along the perimeter of the square. The two new functions we define will be called square-sine and square-cosine. Let square-sin(t) he equal to the y-coordinate of the point where the person stops on the square, and let square-cos(t) be equal to the x-coordinate of the point where the person stops on the square. For example, square-sin(1) = 1/2. Find the values of square-sin(1/2), square-sin(-7/2), square-sin(26), square- cos(-1), square-cos(-151/2), and square-cos(62). Make a sketch of the square-sine function. Is this function periodic? If so, what is the period? What are the domain and the range of this function? Sketch the square-cosine function. Can the square-sine function be shifted to obtain the square-cosine function? If so, write an equation to express this relationship.

Solution

t= 4 we reach the intial position

a) square sine (1/2) = 1/2

square sine (-7/2 ) : t = -3.5 = -3 -1/2

So,sin(-7/2) = sin(1/2) = 1/2

square sin26; t = 26 = 24 + 2 = 2

square sin26 =sin2 = 0

square cos(-151/2) :

t = -151/2 = 75.5 = 72 +3.5 = 0.5

square cos(-151/2) = 1/2

square cos(-1) = 0

square cos 62 = 60+2 = square cos2 = -1/2