Graphs of Sine and Cosine Trigonometry Functions

[nycmathguy]

Section 4.5

I know how to draw one full period of the trigonometric functions listed above but not so sure about two full periods. How is this done by hand.

Also, what is easiest way to graph g(x) for question 28?

Note: Don't tell me to use Desmos. If I use Desmos, I take no credit.

 

[MathLover1]

note:
Amplitude of f(x)=sin (x) is 1
Amplitude of f(x)=cos (x) is 1
Period of f(x)=sin (x) is 2π
Period of f(x)=cos (x) is 2π
Period of f(x)=tan (x) is π
Period of f(x)=cot (x) is π
Period of f(x)=sec( x) is 2π
Period of f(x)=csc(x) is 2π

you have to include two periods

to graph by hand, make a table, choose several values for x, calculate f(x), plot the points and draw a curve through

 

[nycmathguy]

note:
Amplitude of f(x)=sin (x) is 1
Amplitude of f(x)=cos (x) is 1
Period of f(x)=sin (x) is 2π
Period of f(x)=cos (x) is 2π
Period of f(x)=tan (x) is π
Period of f(x)=cot (x) is π
Period of f(x)=sec( x) is 2π
Period of f(x)=csc(x) is 2π

you have to include two periods

to graph by hand, make a table, choose several values for x, calculate f(x), plot the points and draw a curve through

1. Can you provide several pi values for x for me to form a table?

2. Can you do g(x) for question 28?


3. What does it mean to include two periods?


4. Can you provide the steps for graphing g(x) for question 28?

Note: We are going to take it easy moving forward. Less questions leads to extended discussions. No need for me to be anxious about reaching calculus 1. Mathematics is a just a hobby for me.

 

[MathLover1]

1. Can you provide several pi values for x for me to form a table?

x=0,1,2,3.......,12 (two periods are 4pi approximately 12.6)


2. Can you do g(x) for question 28?

the procedure for g(x) is same as for f(x)

3. What does it mean to include two periods?
include two periods means 4pi
from 0 to 4pi
|0...........pi,...........2pi,...........3pi,...........4pi

4. Can you provide the steps for graphing g(x) for question 28?

form a table
x|.......0...1....2...3.......,12
f(x)| ..? ..?
plot the points and draw a cos curve through

 

[nycmathguy]

1. Can you provide several pi values for x for me to form a table?

x=0,1,2,3.......,12 (two periods are 4pi approximately 12.6)


2. Can you do g(x) for question 28?

the procedure for g(x) is same as for f(x)

3. What does it mean to include two periods?
include two periods means 4pi
from 0 to 4pi
|0...........pi,...........2pi,...........3pi,...........4pi

4. Can you provide the steps for graphing g(x) for question 28?

form a table
x|.......0...1....2...3.......,12
f(x)| ..? ..?
plot the points and draw a cos curve through

Ok. I will work on this on my days off.

 

[nycmathguy]

note:
Amplitude of f(x)=sin (x) is 1
Amplitude of f(x)=cos (x) is 1
Period of f(x)=sin (x) is 2π
Period of f(x)=cos (x) is 2π
Period of f(x)=tan (x) is π
Period of f(x)=cot (x) is π
Period of f(x)=sec( x) is 2π
Period of f(x)=csc(x) is 2π

you have to include two periods

to graph by hand, make a table, choose several values for x, calculate f(x), plot the points and draw a curve through

Note:

This weekend we continue our precalculus trek. I plan to graph several trigonometric functions by hand (no more than 6). Section 4.5 is all about the sine and cosine functions. I will concentrate on those two. I can easily use Desmos but graphing by hand is not a bad skill to learn (review in my case). I took precalculus as an elective course at Lehman College in the Spring 1993 semester. I got an A minus. Of course, this is long ago.

 

[nycmathguy]

note:
Amplitude of f(x)=sin (x) is 1
Amplitude of f(x)=cos (x) is 1
Period of f(x)=sin (x) is 2π
Period of f(x)=cos (x) is 2π
Period of f(x)=tan (x) is π
Period of f(x)=cot (x) is π
Period of f(x)=sec( x) is 2π
Period of f(x)=csc(x) is 2π

you have to include two periods

to graph by hand, make a table, choose several values for x, calculate f(x), plot the points and draw a curve through

Question 26

Question 28

Question 30

Note: I only graphed one cycle.

 

[MathLover1]

good job

 

[nycmathguy]

good job

Thanks. It's taking too long to graph by hand. I like it but there are more important math skills to develop, especially applications.