0
$\begingroup$

I am attempting to do my homework but my book got lost in the mail, I have a test on Monday, and I only have the homework problems and my meticulous notes from class.

The next set of homework asks for the exact circular function value for $\sin (7\pi/6)$.

How do I figure this out without a calculator or diagram?

  • 1
    Do you know how to calculate $\sin(\pi+\theta)?$2011-06-11
  • 0
    No, I do not know what that means.2011-06-11
  • 0
    @Adam: you may want to read [this](http://en.wikipedia.org/wiki/List_of_trigonometric_identities).2011-06-11
  • 0
    I was just going through that, does that mean I have to memorize them all?2011-06-11
  • 0
    @Jack: Adam has been referred to Wikipedia's identities a number of times now. @Adam: I thought you just had a test? (http://math.stackexchange.com/questions/44653/tan-sec-test-questions)... Adam: You seem to be asking the same sorts of questions repeatedly, showing very little learning from answers that have been provided, repeatedly, or from links you've been provided, or geometric interpretations, etc. Are you asking for more answers?2011-06-11
  • 0
    We have a test every 4 days or so, it is a 4 week class. Anyways I don't recall asking any questions on circular functions, as I have not gotten to this homework yet. But yeah I am having troubles with easy high school math in college, I must be stupid and lazy.2011-06-11
  • 0
    @Adam: berating yourself isn't going to help. As long as you believe such things about yourself, it's too easy to "cop out" and stop trying. Many user's have tried to help; there are resources that you have been directed to, and you seem to argue with users trying to help. And...a large percent of the time, you have not accepted answers, or voted them up?2011-06-11
  • 0
    @Jack: I'm sorry if it came across as a criticism of *you*, in my earlier post; I simply wanted to alert you to some background issues here, as an FYI, so to speak.2011-06-11
  • 0
    @amWhy: Hmm, good point. I didn't notice Adam's previous question. Now I see that the background issues are not trivial. For answering the questions, one should consider such issue. One the other hand, a reasonable information about the background, motivation provided by the OP may be helpful.2011-06-11
  • 0
    @Jack: absolutely; I really do try to give OPs the benefit of any doubt.2011-06-11
  • 0
    @Adam: What do you mean by "circular function"?2011-06-11
  • 0
    @Adam: re: circular functions...do you mean polar coordinates? (e.g. representing points using radius and angle? I'd like to help, if you could clarify that, or else, if you have another question, that requires "circular function", post it as a question, with some clarification/an example, what you know, what you don't know, etc...and I'll try and clarify...Please understand that I didn't mean to "scold you" earlier...It just helps to get answers when you can show what you do know, where you're stuck, etc...I think you know more than you realize you know...but don't trust yourself!2011-06-12
  • 0
    Circular functions in my book are when r=1 so sin is y cos is x etc.2011-06-12
  • 0
    @Adam: got it...that makes sense: the unit circle/r=1.2011-06-12

1 Answers 1

1

You don't have to memorize all of the stuff on the wikipedia page to figure out this sort of thing. For this question, you should know that $\sin(\pi/6)=1/2$ and either remember that $\sin(\pi + \theta)=-\sin(\theta)$ for any angle $\theta$, or be able to figure this out by remembering the graph of $\sin(\theta)$ and staring at the graph for a second or two. (I favour the latter approach). Or you can draw a unit circle and figure things out that way.

Anyway, taking $\theta=\pi/6$ in the formula $\sin(\pi+\theta)=-\sin(\theta)$, we get $\sin(7\pi/6)=\sin(\pi + \pi/6)=-\sin(\pi/6)=-1/2$.

If you think it's likely you'll be asked this kind of question, I would advise memorizing the values of $\sin$ and $\cos$ at $\pi/6$ and $\pi/3$ along with the graphs of $\sin$ and $\cos$, and practise using this to figure out other values of trig functions at various other angles.

  • 0
    I have all the values memorized in degrees, should I bother memorizing radians or just convert them all to degrees?2011-06-11
  • 0
    @Adam: good advice here. Realize that $\pi/6 = 30^\circ$. Try to develop some "fluency" with the most common angle measures: degrees <-> radians. (Simply remembering 360 degrees = $2\pi$ radians will help; from that, 180 degrees = $\pi$ radians, 90 degrees = $\pi/2$ radians, so 30 degrees is 1/3 of 90 degrees, hence 30 degrees is 1/3 of $\pi/2 = \pi/6$ radians, etc.2011-06-11
  • 0
    If it's easier for you to work with degrees, that's fine. But you'll want to be able to convert from radians to degrees, yes? And back again to radians (if that's what a test question requires).2011-06-11
  • 0
    I can convert both ways and I have a basic understanding of radians.2011-06-11
  • 0
    @Adam: good! Then it's fine to work with degrees, if you're more comfortable with degrees, and values of trig functions of angles given in degrees.2011-06-11