Expert: Paul Klarreich - 12/7/2008

Question
QUESTION: For 1-9, Can you please do me a huge favor and tell me step-by-step for each question what to type into either quickmath.com, calculator.com or mathway.com (whichever you think is best) to get the answers? I need to make sure that they are worked out fully.. Thanks.


Determine the amplitude of each function, then graph the function y = sin x in the same rectangular coordinate system for 0 < x < 2 PIE

{Need a graph}

1) y = 5 sin x

ANSWER: The amplitude is 5


Determine the amplitude and period of each function, then graph one period of the function.

{Need a graph}

2) y = sin 4x

ANSWER: Amplitude = 1  Period = 2pi/4 or pi/2


Determine the amplitude, period and phase shift of the function, then graph one period of the function.

{Need the phase, and graph}

3) y = sin (x - PIE over 2)


ANSWER: Amplitude = 1   T = 2pi/1 or 2pi   f = (pi/2)


Determine the amplitude of each function, then graph the function and y = cos x in the same rectangular coordinate system for 0 < x <2 PIE

4) y = 3 cos x

{Need a graph}

ANSWER: Amplitude = 3


Determine the amplitude and period of each function, then graph one period of the function.

5) y = cos 4x

ANSWER: Amplitude = 1   T = 2pi/4 or pi/2

6) Determine the amplitude, period, and phase shift of the function, then graph one period of the function.

{Need a graph}

6) y = cos (x + PIE over 2)

ANSWER: Amplitude = 1  T = 2pi  f = (-pi/2)


Graph two periods of the given tangent function.

{Need 2 graphs}

7) y = 2 tan x / 4

ANSWER: period = pi/(1/4) or 4pi


Graph two periods of the given cotangent function.

{2 graphs}

8) y = 1/2 cot x

ANSWER: Period = pi


Graph two periods of the given cosecant or secant function.

{Need 2 graphs}

9) y = 2 csc x

ANSWER: p = 2pi


ANSWER: Questioner:   Andy
Category:  Advanced Math
Private:  Yes
 
Subject:  graphs and trig
Question:  For 1-9, Can you please do me a huge favor and tell me step-by-step for each question what to type into either quickmath.com, calculator.com or mathway.com (whichever you think is best) to get the answers?

>> Sorry, I never heard of them.


I need to make sure that they are worked out fully.. Thanks.


Determine the amplitude of each function, then graph the function y = sin x in the same rectangular coordinate system for 0 < x < 2 PIE

{Need a graph}

1) y = 5 sin x

ANSWER: The amplitude is 5


Determine the amplitude and period of each function, then graph one period of the function.

{Need a graph}

2) y = sin 4x

ANSWER: Amplitude = 1  Period = 2pi/4 or pi/2


Determine the amplitude, period and phase shift of the function, then graph one period of the function.

{Need the phase, and graph}

3) y = sin (x - PIE over 2)


ANSWER: Amplitude = 1   T = 2pi/1 or 2pi   f = (pi/2)


Determine the amplitude of each function, then graph the function and y = cos x in the same rectangular coordinate system for 0 < x <2 PIE

4) y = 3 cos x

{Need a graph}

ANSWER: Amplitude = 3


Determine the amplitude and period of each function, then graph one period of the function.

5) y = cos 4x

ANSWER: Amplitude = 1   T = 2pi/4 or pi/2

6) Determine the amplitude, period, and phase shift of the function, then graph one period of the function.

{Need a graph}

6) y = cos (x + PIE over 2)

ANSWER: Amplitude = 1  T = 2pi  f = (-pi/2)


Graph two periods of the given tangent function.

{Need 2 graphs}

7) y = 2 tan x / 4

ANSWER: period = pi/(1/4) or 4pi


Graph two periods of the given cotangent function.

{2 graphs}

8) y = 1/2 cot x

ANSWER: Period = pi


Graph two periods of the given cosecant or secant function.

{Need 2 graphs}

9) y = 2 csc x

ANSWER: p = 2pi
.............................................

You seem to be doing OK, and yuo shouldn't have any trouble graphing them if you keep this in mind:

The general form of a sinusoidal function is:

f(x) = A sineorcosine ( fx - b)

where the things have names, and you graph them this way:

1. Draw the basic shape of sine or cosine in one cycle.
2. A is the amplitude.  Label the top of the curve A, label the bottom -A.
3. f is the frequency. The PERIOD, p, is the solution to the equation:  fx = 2 pi.  Label the end of the cycle p, label the middle p/2, whatever it is.
4. The phase shift is the solution to the equation  fx - b = 0.  Shift the graph to the left or right.

Send me ONE OR TWO of these, and I'll try to help.

Note: Don't mark 'Private'. I change it anyway. If you don't want anyone on this site to see the question, send it somewhere else.


---------- FOLLOW-UP ----------

QUESTION: Using mathway.com...

I need to make sure that they are worked out fully.. Thanks.


Determine the amplitude of each function, then graph the function y = sin x in the same rectangular coordinate system for 0 < x < 2 PIE

{Need a graph}

1) y = 5 sin x

ANSWER: The amplitude is 5


Determine the amplitude and period of each function, then graph one period of the function.

{Need a graph}

2) y = sin 4x

ANSWER: Amplitude = 1  Period = 2pi/4 or pi/2  

Answer
1) y = 5 sin x

ANSWER: The amplitude is 5

>. There is nothing to work out.

A. Draw the basic sine shape (carefully, of course -- same as you do anything else.)
B. A = 5.  Label top +5, and bottom -5.
C. P = 2 pi. Label right end = 2 pi, middle 1 pi.



Determine the amplitude and period of each function, then graph one period of the function.

{Need a graph}

2) y = sin 4x

ANSWER: Amplitude = 1  Period = 2pi/4 or pi/2


A. Draw the basic sine shape (carefully, of course -- same as you do anything else.)
B. A = 1.  Label top and bottom.
C. P = pi/2. Label right end = pi/2, middle pi/4.

(see attached graph)