Trigonometry graphing question

Question

Hello! I'm having some trouble graphing the following and would like someone to help me with it, please.

Graph  on [-4π, 4π] and verbalize how the graph varies from the graphs of . 

Graph  on the window [−5π, 5π] and describe freely what the graph shows.

I'm currently using symbolab (https://www.symbolab.com/graphing-calculator) to do it but I'm stuck in the first graph. It would be amazing to get help from someone to graph both equations.

When i put f(x) = x sin x on symbolab it seems to be a beginning but as I'm not being able to find the point of local maxima and minima I can't proceed.

Any help is welcome!

Thank you in advance!!!

Answer 1

From my calculator I enter xsin(x); -15.71, 15.71 (this is 5pi).

I get the top side (small end) of an oval. The top point is 0,.0171.

This is the best I can do.

Answer 2

I would recommend to graph functions like these at

www dot desmos dot com

Note that for the second function X=0 is NOT in the domain,

as it causes division by zero. THAT may be the problem

with your software graph.

In the meantime here are two tables for these two functions

x f(x)

-12.56637061 0.00000 x f(x)

-11.78097245 -8.33041 -15.70796327 0.000000

-10.99557429 -10.99557 -14.9225651 0.047385

-10.21017612 -7.21968 -14.13716694 0.070736

-9.424777961 0.00000 -13.35176878 0.052960

-8.639379797 6.10896 -12.56637061 0.000000

-7.853981634 7.85398 -11.78097245 -0.060021

-7.068583471 4.99824 -10.99557429 -0.090946

-6.283185307 0.00000 -10.21017612 -0.069255

-5.497787144 -3.88752 -9.424777961 0.000000

-4.71238898 -4.71239 -8.639379797 0.081847

-3.926990817 -2.77680 -7.853981634 0.127324

-3.141592654 0.00000 -7.068583471 0.100035

-2.35619449 1.66608 -6.283185307 0.000000

-1.570796327 1.57080 -5.497787144 -0.128617

-0.785398163 0.55536 -4.71238898 -0.212207

4.44089E-15 0.00000 -3.926990817 -0.180063

0.785398163 0.55536 -3.141592654 0.000000

1.570796327 1.57080 -2.35619449 0.300105

2.35619449 1.66608 -1.570796327 0.636620

3.141592654 0.00000 -0.785398163 0.900316

3.926990817 -2.77680 0.000000 #DIV/0!

4.71238898 -4.71239 0.785398163 0.900316

5.497787144 -3.88752 1.570796327 0.636620

6.283185307 0.00000 2.35619449 0.300105

7.068583471 4.99824 3.141592654 0.000000

7.853981634 7.85398 3.926990817 -0.180063

8.639379797 6.10896 4.71238898 -0.212207

9.424777961 0.00000 5.497787144 -0.128617

10.21017612 -7.21968 6.283185307 0.000000

10.99557429 -10.99557 7.068583471 0.100035

11.78097245 -8.33041 7.853981634 0.127324

12.56637061 0.00000 8.639379797 0.081847

9.424777961 0.000000

10.21017612 -0.069255

10.99557429 -0.090946

11.78097245 -0.060021

12.56637061 0.000000

13.35176878 0.052960

14.13716694 0.070736

14.9225651 0.047385

15.70796327 0.000000

Answer 3

James -

Unfortunately we cannot attach images, but I hope that you are able to utilize the SymboLab software to follow along.

Let's start with your first problem (you can use Wolframalpha as a backup for graphing, see links below):

1. graph f(x) = x*sin(x) from [-4π, 4π]
2. https://www.wolframalpha.com/input/?i=y+%3D+x*sin%28x%29%2C+y+%3D+x%2C+y+%3D+-x%2C+x+from+-4*pi+to+4*pi
3. What we see here is the standard oscillations we see in a typical graph of sin(x), with a weighting factor of x. If you are able to also graph f(x) = x and f(x) = -x in your software you will see that the oscillations grow bounded by the two lines representing these functions.
4. This aligns with our intuition, which tells us that sin(x) oscillates between -1 and 1. When multiplied by x we see the function oscillate between -x and x
5. For the sin function, we anticipate roots for all multiples of pi and local min / max at all multiples of pi/2. These maxes will always be solutions to the set of functions! In other words, you will have local mins / maxes in all places where y = x*sin(x) intersects with the lines y = x or y = -x!
6. The graph will grow proportionally by x in both the -x and +x directions. As x approaches infinity, so does y
7. For your second problem f(x) = sin(x) / x we expect exactly the inverse to occur:
8. https://www.wolframalpha.com/input/?i=y+%3D+sin%28x%29%2Fx%2C+x+from+-5*pi+to+5*pi
9. The one unique thing to note here is that we spike up to infinity for x = 0. This is because functions don't like to be divided by zero
10. You will still see roots for all multiplex of pi
11. Because we are now scaling by 1/x our sin function will become more and more flat as we approach infinity.
12. Our local mins and maxes still coincide with all multiples of pi / 2, but will never exceed [-1,1]

Good luck!