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anonymous
 one year ago
Determine the sign of sin five pi divided by four without using a calculator.
anonymous
 one year ago
Determine the sign of sin five pi divided by four without using a calculator.

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welshfella
 one year ago
Best ResponseYou've already chosen the best response.1dw:1435357223930:dw

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Can you explain to me how to find that? @welshfella :)

welshfella
 one year ago
Best ResponseYou've already chosen the best response.1what is the sign of opposite / hypotenuse from the diagram

welshfella
 one year ago
Best ResponseYou've already chosen the best response.1positive angles go anticlockwise one half a rev is pi and 5pi/4 is another p/4 the signs of the lines are marked

welshfella
 one year ago
Best ResponseYou've already chosen the best response.1sin 5pi/4 =  / + = 

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Both hypotenuse and opposite are negative.

welshfella
 one year ago
Best ResponseYou've already chosen the best response.1No hypotenuse is always positive

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Oops! I was looking at the wrong part. That was the adj.

welshfella
 one year ago
Best ResponseYou've already chosen the best response.1yes the tangent is positive / in 3rd quadrant

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0"positive angles go anticlockwise" what do you mean by this?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0So 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
 one year ago
Best ResponseYou've already chosen the best response.1they are measured in an anticlockwise direction angles measured in clockwise direction are negative  that the convention 5pi/4 is equivalent to 3pi/4

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0\[\sin \frac{ 5 \pi }{ 4 }=\sin \left( \pi+\frac{ \pi }{ 4 } \right)=\sin \frac{ \pi }{ 4 }=\frac{ 1 }{ \sqrt{2} }\]

welshfella
 one year ago
Best ResponseYou've already chosen the best response.1well i've done it using the unit circle . You can also use identities to do these just as surjithayer has just done.

welshfella
 one year ago
Best ResponseYou've already chosen the best response.1the 1 / sqrt2 comes from the standard triangle dw:1435358195274:dw

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0@surjithayer How did you get \[\sin \pi/4?\]

welshfella
 one year ago
Best ResponseYou've already chosen the best response.1sin pi/4 = 1/sqrt2 therefor  sin pi/4 = 1/sqrt2

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0\[\sin \left( \pi+\beta \right)=\sin \beta \] sin is negative in 3rd quadrant.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Thanks for the help! @surjithayer @welshfella . I'm still kinda confused, but I think I get it now. :)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0\[\sin \left( \pi+x \right)=\sin \pi \cos x+\cos \pi \sin x\] \[\sin \pi=0,\cos \pi=1\]

welshfella
 one year ago
Best ResponseYou've already chosen the best response.1its just a personal thing but I find it easier to use diagrams for this type of problem

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0@welshfella maybe to visualize the problem? Both ways suit for me though. :)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0If 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
 one year ago
Best ResponseYou've already chosen the best response.0Will it be positive?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0yes it is in 3rd quadrant

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Okay, so can I also assume that cos 5pi/4 is negative based on the All Students Take Calculus?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0in 3rd quadrant only tan and cot are positive.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Yes, since cot is just the reciprocal of tan. :)
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