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amorfide
Group Title
I need someone to explain the CAST diagram to me please?
I need to know how to find all possible angles between 360 and 360
for sin
cosin
and
tan
 2 years ago
 2 years ago
amorfide Group Title
I need someone to explain the CAST diagram to me please? I need to know how to find all possible angles between 360 and 360 for sin cosin and tan
 2 years ago
 2 years ago

This Question is Closed

asnaseer Group TitleBest ResponseYou've already chosen the best response.1
It is explained quite well in this video: http://www.youtube.com/watch?v=FpjWXKbCC3w
 2 years ago

amorfide Group TitleBest ResponseYou've already chosen the best response.1
@asnaseer thank you but what i need is lets say we have sinx=0.5 x=sin^1(0.5) i need to know how to get all possible angles
 2 years ago

asnaseer Group TitleBest ResponseYou've already chosen the best response.1
ok, what you need to do in this specific case is note that the primary solution to:\[\sin(x)=0.5\]is:\[x=30^0=\frac{\pi}{6}\]Now, using CAST we also know that:\[\sin(x)=\sin(\pix)\]therefore:\[x=\frac{\pi}{6}\text{ or }x=\frac{5\pi}{6}\]Next note that the sine curve repeats itself every \(2\pi\), so the general solution would be:\[x=\frac{\pi}{6}+2n\pi\text{ for }n=\infty,...,1,0,1,...,\infty\]and:\[x=\frac{5\pi}{6}+2n\pi\text{ for }n=\infty,...,1,0,1,...,\infty\]
 2 years ago

asnaseer Group TitleBest ResponseYou've already chosen the best response.1
I hope that makes sense?
 2 years ago

amorfide Group TitleBest ResponseYou've already chosen the best response.1
it made sense until you brought n into this... what is n exactly?
 2 years ago

asnaseer Group TitleBest ResponseYou've already chosen the best response.1
n is just an integer that can take on any value from \(\infty\) to \(+\infty\). e.g. if n=0, we get:\[x=\frac{\pi}{6}\text{ or }x=\frac{5\pi}{6}\]All n does is add (or subtract) \(2\pi\) to this answer depending on whether n is positive or negative.
 2 years ago

asnaseer Group TitleBest ResponseYou've already chosen the best response.1
that should say "add (or subtract) multiples of \(2\pi\)..."
 2 years ago

amorfide Group TitleBest ResponseYou've already chosen the best response.1
but i have never seen a question give me a value of n? so how would i find values for cosin? cos(x)=0.5 x=cos^1(0.5)
 2 years ago

asnaseer Group TitleBest ResponseYou've already chosen the best response.1
If you haven't been introduced to this general form of the answer, then ignore it for now. So the solutions to your first question would just be:\[x=\frac{\pi}{6}\text{ or }x=\frac{5\pi}{6}\] Now for the second question, first tel me what you think the primary solution is to:\[\cos(x)=0.5\]
 2 years ago

asnaseer Group TitleBest ResponseYou've already chosen the best response.1
Hang on  you are supposed to find solutions between 360 and +360, correct?
 2 years ago

amorfide Group TitleBest ResponseYou've already chosen the best response.1
yes 360 to 360 sorry helping others too
 2 years ago

amorfide Group TitleBest ResponseYou've already chosen the best response.1
i know how to convert to radians
 2 years ago

asnaseer Group TitleBest ResponseYou've already chosen the best response.1
So first draw these two solutions we found as follows: dw:1349974770993:dw
 2 years ago

asnaseer Group TitleBest ResponseYou've already chosen the best response.1
So then the negative angles that also satisfy the first equation will be: dw:1349974926971:dw
 2 years ago

asnaseer Group TitleBest ResponseYou've already chosen the best response.1
Does that make sense?
 2 years ago

amorfide Group TitleBest ResponseYou've already chosen the best response.1
the 210 makes sense, the 330 does not
 2 years ago

asnaseer Group TitleBest ResponseYou've already chosen the best response.1
360 + 150 = 210 360 + 30 = 330
 2 years ago

asnaseer Group TitleBest ResponseYou've already chosen the best response.1
dw:1349975262412:dw
 2 years ago

asnaseer Group TitleBest ResponseYou've already chosen the best response.1
dw:1349975300819:dw
 2 years ago

asnaseer Group TitleBest ResponseYou've already chosen the best response.1
Does that help?
 2 years ago

amorfide Group TitleBest ResponseYou've already chosen the best response.1
okay so sin is fine cosine?
 2 years ago

asnaseer Group TitleBest ResponseYou've already chosen the best response.1
Exactly the same principles
 2 years ago

asnaseer Group TitleBest ResponseYou've already chosen the best response.1
dw:1349975392520:dw
 2 years ago

amorfide Group TitleBest ResponseYou've already chosen the best response.1
thank you! you are like my hero i can do most of the complicated things but this was always just too hard :P i understand it better now, thank you!
 2 years ago

asnaseer Group TitleBest ResponseYou've already chosen the best response.1
you are more than welcome my friend! I'm glad I was able to explain it to you. :)
 2 years ago
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