anonymous
  • anonymous
Determine the sign of sin five pi divided by four without using a calculator.
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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welshfella
  • welshfella
|dw:1435357223930:dw|
anonymous
  • anonymous
Can you explain to me how to find that? @welshfella :)
welshfella
  • welshfella
what is the sign of opposite / hypotenuse from the diagram

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More answers

welshfella
  • welshfella
positive angles go anticlockwise one half a rev is pi and 5pi/4 is another p/4 the signs of the lines are marked
welshfella
  • welshfella
sin 5pi/4 = - / + = -
anonymous
  • anonymous
Both hypotenuse and opposite are negative.
welshfella
  • welshfella
No hypotenuse is always positive
anonymous
  • anonymous
Oops! I was looking at the wrong part. That was the adj.
welshfella
  • welshfella
yes the tangent is positive -/- in 3rd quadrant
anonymous
  • anonymous
"positive angles go anticlockwise" what do you mean by this?
anonymous
  • anonymous
So the answer would be negative, right? But can you explain to me the steps how to find it? I'm so confused right now. Like what do I need to do first?
welshfella
  • welshfella
they are measured in an anticlockwise direction angles measured in clockwise direction are negative - that the convention 5pi/4 is equivalent to -3pi/4
anonymous
  • anonymous
\[\sin \frac{ 5 \pi }{ 4 }=\sin \left( \pi+\frac{ \pi }{ 4 } \right)=-\sin \frac{ \pi }{ 4 }=-\frac{ 1 }{ \sqrt{2} }\]
welshfella
  • welshfella
well i've done it using the unit circle . You can also use identities to do these just as surjithayer has just done.
welshfella
  • welshfella
the 1 / sqrt2 comes from the standard triangle |dw:1435358195274:dw|
anonymous
  • anonymous
@surjithayer How did you get \[-\sin \pi/4?\]
welshfella
  • welshfella
sin pi/4 = 1/sqrt2 therefor - sin pi/4 = -1/sqrt2
anonymous
  • anonymous
\[\sin \left( \pi+\beta \right)=-\sin \beta \] sin is negative in 3rd quadrant.
anonymous
  • anonymous
Thanks for the help! @surjithayer @welshfella . I'm still kinda confused, but I think I get it now. :)
welshfella
  • welshfella
yw
anonymous
  • anonymous
\[\sin \left( \pi+x \right)=\sin \pi \cos x+\cos \pi \sin x\] \[\sin \pi=0,\cos \pi=-1\]
welshfella
  • welshfella
its just a personal thing but I find it easier to use diagrams for this type of problem
anonymous
  • anonymous
@welshfella maybe to visualize the problem? Both ways suit for me though. :)
welshfella
  • welshfella
that s good
anonymous
  • anonymous
If I change sin five pi divided by four to, let's say, \[\tan \frac{5\pi }{ 4 }\], what will be the answer? I just want to practice haha.
anonymous
  • anonymous
Will it be positive?
anonymous
  • anonymous
yes it is in 3rd quadrant
anonymous
  • anonymous
Okay, so can I also assume that cos 5pi/4 is negative based on the All Students Take Calculus?
anonymous
  • anonymous
yes
anonymous
  • anonymous
in 3rd quadrant only tan and cot are positive.
anonymous
  • anonymous
Yes, since cot is just the reciprocal of tan. :)

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