# Two short Questions

• Jan 28th 2010, 07:08 AM
derek445
Two short Questions
-Question 1
State the number of cycles in every 360 degrees for the function y=sin3x

-Question 2
Write out explicitly what is meant by $\displaystyle \sum$, above the sum is x=5, to the right of sum is $\displaystyle x^5$ and below is x=1. I had no clue how to do this on LaTex.

I have similar questions to these for an assignment so if you could post the answers so I could do the others, that would be great.
• Jan 29th 2010, 02:57 AM
Hello derek445

Welcome to Math Help Forum!
Quote:

Originally Posted by derek445
-Question 1
State the number of cycles in every 360 degrees for the function y=sin3x

-Question 2
Write out explicitly what is meant by $\displaystyle \sum$, above the sum is x=5, to the right of sum is $\displaystyle x^5$ and below is x=1. I had no clue how to do this on LaTex.

I have similar questions to these for an assignment so if you could post the answers so I could do the others, that would be great.

Question 1:

$\displaystyle \sin x$ has one complete cycle every $\displaystyle 360^o$. As $\displaystyle x$ goes from $\displaystyle 0^o$ to $\displaystyle 360^o, \;3x$ goes from $\displaystyle 0^o$ to $\displaystyle 3\times360^o$, and so $\displaystyle \sin 3x$ will have $\displaystyle 3$ complete cycles.

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Question 2:

To find the meaning of $\displaystyle \sum_{x=1}^{x=5}x^5$, you give $\displaystyle x$ the values (one at a time) $\displaystyle 1, 2, 3, 4, 5$ in the expression after the $\displaystyle \sum$ sign, and add the results together. ($\displaystyle \sum$ is the Greek letter corresponding to 'S', standing for the word 'sum'.)

So:
$\displaystyle \sum_{x=1}^{x=5}x^5=1^5+2^5+3^5+4^5+5^5$