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amorfide
 4 years ago
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
amorfide
 4 years ago
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

This Question is Closed

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

amorfide
 4 years ago
Best 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

asnaseer
 4 years ago
Best ResponseYou've already chosen the best response.1ok, 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:\[x=\frac{5\pi}{6}+2n\pi\text{ for }n=\infty,...,1,0,1,...,\infty\]

asnaseer
 4 years ago
Best ResponseYou've already chosen the best response.1I hope that makes sense?

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

asnaseer
 4 years ago
Best ResponseYou've already chosen the best response.1n 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.

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

amorfide
 4 years ago
Best ResponseYou've already chosen the best response.1but 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)

asnaseer
 4 years ago
Best ResponseYou've already chosen the best response.1If 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:\[\cos(x)=0.5\]

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

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

amorfide
 4 years ago
Best ResponseYou've already chosen the best response.1i know how to convert to radians

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

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

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

asnaseer
 4 years ago
Best ResponseYou've already chosen the best response.1360 + 150 = 210 360 + 30 = 330

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

asnaseer
 4 years ago
Best ResponseYou've already chosen the best response.1Exactly the same principles

amorfide
 4 years ago
Best ResponseYou've already chosen the best response.1thank 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!

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