anonymous
  • anonymous
what is tan of 2pi/3 also what is the csc of pi/4 (sorry still a bit confused)
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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Psymon
  • Psymon
Do you have a unit circle handy on you to help ya out with this?
anonymous
  • anonymous
yes im looking at it. but I lost the one that has all my notes :(
Psymon
  • Psymon
Ah x_x Well, let's start out with knowing that tangent is the same and sin divided by cosine. SO if we want tangent of 2pi/3, we take the sin of 2pi/3 and divide it by the cos 2pi/3. If you can look up those values then we can find out what that is : )

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Psymon
  • Psymon
\[\frac{ \sin(\frac{ 2\pi }{ 3 }) }{ \cos (\frac{ 2\pi }{ 3 }) }\]
anonymous
  • anonymous
sin of 2pi/3 is \[\sqrt{3}\div2\] and the cos is -1/2
Psymon
  • Psymon
Correct. so now divide those 2: \[\frac{ \frac{ \sqrt{3} }{ 2 } }{ \frac{ -1 }{ 2 } } \]
Psymon
  • Psymon
Or simply: \[\frac{ \sqrt{3} }{ 2 }*-2 \]
anonymous
  • anonymous
so would it be -sqrt of 6?
Psymon
  • Psymon
Nope. Just cancel out the two on top and bottom in what I have posted above.
Psymon
  • Psymon
|dw:1378178187538:dw|
anonymous
  • anonymous
oooohhhhh! that makes sense! so I would just do the same for csc of pi/4? it would be 1/ sqrt2/2 so itd just be the sqrt2/2??
Psymon
  • Psymon
Not quite. |dw:1378178364325:dw|
anonymous
  • anonymous
oh yeah you have to get rid of the sqrt on the bottom! its all coming back slowly but surley! Thank you !
Psymon
  • Psymon
Lol, np ^_^
Psymon
  • Psymon
Depending on your teacher, a lot of the times in calculus no-one cares if you rationalize the denominator, lol.
anonymous
  • anonymous
wait I want to try another one with you to make sure im getting it is that okay ?
Psymon
  • Psymon
No problem
anonymous
  • anonymous
so this one is sec of 4pi/3...|dw:1378178743424:dw|
anonymous
  • anonymous
\[\tan (\cos^{-1} (-\sqrt{3}\div2)) how do you do this ?
Psymon
  • Psymon
Okay, so cos of 4pi/3 = -1/2. And then if we flip that by doing 1/(-1/2), we get sec 4pi/3 to be -2. I can't quite see what you just typed up, though. Lemme refresh and see fi I can see it.
anonymous
  • anonymous
I got -2 as my answer
Psymon
  • Psymon
Okay, I think you put this (cant tell, not seeing any equation editor stuff) \[\tan(\cos^{-1} (-\frac{ \sqrt{3} }{ 2 }))\] And yeah, for the sec 4pi/3 one it is -2 :3
anonymous
  • anonymous
yep that's the problem. do I inverse cos of -sqrt3/2 then find the tan of that ?
Psymon
  • Psymon
Correct. So arccos of -sqrt(3/2) two possible values. The angle of cosine that could get us that might be 5pi/6 or 7pi/6. Since those two values are possible, then youre simply solving for tan(5pi/6) and tan(7pi/6)
anonymous
  • anonymous
would the tan of 5pi/6 be -sqrt 3?
Psymon
  • Psymon
So we would have sin 5pi/6, which is 1/2,divided by cos 5pi/6, which is -sqrt(3)/2. So we have this: |dw:1378179532932:dw|
anonymous
  • anonymous
okay! I get it now! I just keep messing up on simple steps.
Psymon
  • Psymon
Yeah D: Now if we did it with 7pi/6, because we do need to: |dw:1378179765373:dw|
anonymous
  • anonymous
so do I need to have both answers down?
Psymon
  • Psymon
Yes, you do. Because both answers give the correct response.
anonymous
  • anonymous
okay awesome! How do I give you one of those medal thingys ?
Psymon
  • Psymon
Just click best response, lol
anonymous
  • anonymous
Oh I already did that a while ago! hahah ! Thank you soooo much! Hopefully I won't forget!
Psymon
  • Psymon
Yep, no worries, glad ya got it ^_^
anonymous
  • anonymous
:) !!

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