Basic Graphs

[Caitlin0122]

I've been stuck on this problem, and without a textbook it's hard to know specifically what to look up online. I was wondering if anyone could give me a basic idea of what it means by, "the roots are x=". Thank you!

 

[Dr.Peterson]

View attachment 27476
I've been stuck on this problem, and without a textbook it's hard to know specifically what to look up online. I was wondering if anyone could give me a basic idea of what it means by, "the roots are x=". Thank you!

"Root" is another word sometimes used as a synonym for "x-intercept"; in this case both mean "solution to \(\sin(x) = 0\). (I myself only use the word "root" of an equation, not a function; yet another word would be "zero", which does apply to a function, and means the same thing here.)

That should make this a lot easier.

 

[nasi112]

Alternative solution

[MATH]\cos x = 1[/MATH][MATH]\cos x = -1[/MATH]
What are the angles that makes cosine function equal one and negative one? These are the same angles that makes sine function equal zero.

 

[pka]

View attachment 27476
I've been stuck on this problem, and without a textbook it's hard to know specifically what to look up online. I was wondering if anyone could give me a basic idea of what it means by, "the roots are x=".

Use the GRAPH. Try \(x=-2\pi,~-\pi,~0,~\pi,~\&~2\pi\)