period of y = sin(3x) / find values, given period / etc

L

Louise Johnson

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Jan 21, 2007
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103
Again looking for anyone who can have a look at these and let me know if I am on the right track on not.
Thank you
Louise

#1 graph of y=sin 3x

What is the period? and what is the x- coordinate of that point?Answer 2pi/3 so x would equal -1/2


#2 The period of function f is 5. If f(1)=4, f(2)=5, and f(4)=-2, the value of f(7) is ?Answer 5 (This one I drew out as a sine wave and predicted what it would be when it got to 7...Not sure if that was the easiest way.

#3 If 0<Ø<pi and cosØ =0.5, then the value of cos (2Ø) is?[/size] I am having a hard time with this one. Ø is between 0 and pi. cos Ø =1/2 then the value of cos(2Ø) is 1??
 
1)
graph of y=sin 3x
what is the period?
x=0 y=0
3x=2 pi y=0
period is 2/3 pi and x= 2pi/3 at this point

2)
period is 5
we have sets:
1 to 5
6 to 10
11 to 15 etc.

f[1]=f[6]=4
f[2]=f[7]=5
f[4]=f[9]=-2

f[x]=f[x-5] for all x greater than zero I think 1<x<infinity

3)
do you know the formula for the sum of angles?
sin[A+B]=SinAcosB+cosAsinB
cos[A+B]=cosAcosB-sinAsinB

sketch a right triangle. mark the hypoteneuse 1
mark the adjacent side .5
then the opposite side is:
1^2=.5^2+y^2
y=sqrt[3/4]
y=1/2 sqrt3
sin@= 1/2 sqrt3

cos[@+@]=cos@cos@-sin@sin@
cos[2@]=[.5]^2+[1/2 sqrt3]^2
cos2@=1/4 +3/4
cos2@=1

Arthur
 
f[x]=f[x-5] is wrong poor notation on my part
f[x]= f[x-5n] n a integer such that f[x-n] is between 1 and 5
 
Thank you so much

Dear Arthur, Thank you so much for you help. That by far is the best response I have ever gotten. The good news is that I got then all correct however number three appears to be by shear luck. I am still gonna go through each of your explanations some more but I just wanted to say thank you before I missed you!

Wow
thank you
again
Louise
 
For #3.....you can use one of the "double-angle" identities.

cos (2A) = 2 cos<SUP>2</SUP> A - 1

You are given cos A = 0.5, or 1/2.

cos (2A) = 2*(1/2)<SUP>2</SUP> - 1

cos (2A) = 2*(1/4) - 1

cos (2A) = (1/2) - 1

cos (2A) = -1/2

So, I would not agree with your answer to that one.
 
Dear Mrspi, Thank you for going over these. I feel better knowing number three was tricky and it wasn't just me. The double angle identity method seems alot shorter however I will have to look over it some more.
Thanks again
Louise
 
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