Use the method of adding y-coordinates to graph the function on the interval [0, 2π].

Question

(a) use the Product-to-Sum Formulas to express each product as a sum, and (b) use the method of adding y-coordinates to graph the function on the interval [0, 2π].

f (x) = sin (2x) sin x

Answer 1

Step 1 :

(a)

The function is .

Product-to-sum formulas : .

The product can be written as a sum of .

Step 2 :

(b)

The method of adding y - coordinates :

The function is and the interval is .

Consider the composite functions as and .

Comments

Contd........

Make a table of values in the interval :

	0
	0.5	0.3535	0	0.3535	0.3535	0.3535	0.5
	0.5	0.3535	0	0.3535	0.3535	0.3535	0.5
	0	0.707	0	0.707	0.707	0.707	0
Point on the graph of f	(0, 0)

 

Answer 2

Contd..

Graph the functions and on the same coordinate system.

(1) Draw the coordinate plane.

(2) plot the points.

(3) connect the points with a smooth curve.

The graph is :

 

Solution :

(a) .

(b) The graph is :