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This is probably one of the easiest concepts but I do not get it, so I am going to give the two problems that are giving me the most trouble on my very long worksheet I have to do, maybe you guys can help me understand how to do it all.

1.) $\tan(-3π/2)$;

2.) $\cos(17π/3)$

Steps and explanations would be very helpful, thanks and please no judging on my lack of knowledge in math! I said this in the comments below but thought I would put it up here too. My teacher has us writing it out like this, for example, tan(-3π/2)= -y/x=____. We have to write the problem, show that we know the definition (hence the y/x part) and then look on our trig wheel and fill in the x and y coordinates. I don't know why I am confused, I guess I am just having trouble locating it on the trig wheel, but if you know how to work it this way can anyone show me step by step?

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    $\begingroup$ Do you have memorized some very basic values of sin and cos? Say, for $0$, $\pi/6$, $\pi/4$, $\pi/3$, and $\pi/2$? Usually you can reduce most questions you will be asked to those values using some simple trig identities. $\endgroup$
    – Seth
    Commented Apr 15, 2014 at 22:54
  • $\begingroup$ In particular for these problems use the definition of tan and periodicity of cos and sin $\endgroup$
    – Seth
    Commented Apr 15, 2014 at 22:56
  • $\begingroup$ My teacher handed me the trig wheel today so I am in the process of memorizing it all. $\endgroup$ Commented Apr 15, 2014 at 22:56
  • $\begingroup$ The important thing, beyond @Seth’s suggestion, is to remember that in view of the periodicity of $\tan$ and $cos$, you can add or subtract multiples of $\pi$ from the argument of $\tan$ without changing the value, similarly, you can add or subtract multiples of $2\pi$ from the argument of $\cos$. $\endgroup$
    – Lubin
    Commented Apr 15, 2014 at 22:56

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Remember that sin and cos are $2\pi$ periodic. Also remember that cos is even and sin is odd.

$\tan(-3\pi/2)=\frac{\sin(-3\pi/2)}{\cos(-3\pi/2)}=\frac{\sin(\pi/2)}{\cos(\pi/2)}$

$\cos(17\pi/3)=\cos(-\pi/3)=\cos(\pi/3)$

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  • $\begingroup$ Okay thank you and my teacher has us writing it out like this, for example, tan(-3π/2)= -y/x=________. Sorry if that's confusing but we have to write the problem, show that we know the definition (hence the y/x part) and then look on our trig wheel and fill in the x and y coordinates. I don't know why I am confused, I guess I am just having trouble locating it on the trig wheel, but if you know how to work it this way can you show me? $\endgroup$ Commented Apr 15, 2014 at 23:03
  • $\begingroup$ @IlaIsabelle I took precalc a million years ago and have no memory of it (I haven't taught that course yet). All I know are trig identities and the values of sin and cos that I mentioned above. I'm not sure what methods you are learning. $\endgroup$
    – Seth
    Commented Apr 15, 2014 at 23:05
  • $\begingroup$ Oh gotcha, that's fine but thanks for your help! $\endgroup$ Commented Apr 15, 2014 at 23:06

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