Graphing the Cosine Function Help?

Question

In this assignment you will be generating the graph of the cosine curve.  To do this, you should go through the same process we used to generate the sine and the tangent curves. 
1. Using your calculator, complete the table below for the function y = cos x.  Find the corresponding yvalues rounded to the nearest thousandth. 

X

0º

30º

60º

90º

120º

150º

180º

210º

240º

270º

300º

330º

360º

Y

 

X

0º

-30º

-60º

-90º

-120º

-150º

-180º

-210º

-240º

-270º

-300º

-330º

-360º

Y

2.  Plot all the points from the table on a grapgh. Draw the curve.

3. Answer the following questions:

a. What is the domain? 
b. What is the range? 
c. What is the y-intercept? 
d. What are the x-intercepts?

4. Also, answer the following questions as you compare the sine and cosine curves.
a. How are the sine and cosine curves similar?   
b. How are the sine and cosine curves different?  

**Although it is expected that you use a calculator to generate the values, your graph should NOT be done with a graphing utility.  Be sure to show all points generated and the curve that connects them. 

 

Answer 1

(1)

The function is .

Complete the table:

Complete the table:

Answer 2

(2)

Graph:

Graph the function .

Plot the points obtained in the table.

Connect the points using a smooth curve.

Answer 3

(3)

Step 1:

The function is .

The domain of the cosine function is all real numbers.

The range of the function is .

Find the -intercept by substituting in .

.

The -intercept .

Step 2:

Find the -intercept by equating .

, where n is a odd positive integer.

The -intercept is .

Solution:

(a) The domain of the cosine function is all real numbers.

(b) The range of the function is .

(c) The -intercept .

(d) The -intercept is , where n is a odd positive integer.

Answer 4

(4)

a) Similarities between sine and cosine functions:

The domain and range is same for both the functions.

The period is same for both the functions.

b) Difference between sine and cosine functions:

The relationship between the cosine and sine graphs is that the cosine is the same as the sine except that it is shifted to the left by .

The sine function has maximum values at , where n is an integer and minimum values at , where n is an integer.

The cosine function has maximum values at , where n is an integer and minimum values at , where n is an integer.