1. ## 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 $\sum$, above the sum is x=5, to the right of sum is $x^5$ 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.

2. Hello derek445

Welcome to Math Help Forum!
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 $\sum$, above the sum is x=5, to the right of sum is $x^5$ 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:

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

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Question 2:

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

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