Question

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

Answer 1

It is explained quite well in this video: http://www.youtube.com/watch?v=FpjWXKbCC3w

Answer 2

@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

Answer 3

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:\[\sin(x)=\sin(\pi-x)\]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:\[x=\frac{5\pi}{6}+2n\pi\text{ for }n=-\infty,...,-1,0,1,...,\infty\]

Answer 4

I hope that makes sense?

Answer 5

it made sense until you brought n into this... what is n exactly?

Answer 6

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.

Answer 7

that should say "add (or subtract) multiples of \(2\pi\)..."

Answer 8

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)

Answer 9

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:\[\cos(x)=0.5\]

Answer 10

Hang on - you are supposed to find solutions between -360 and +360, correct?

Answer 11

yes -360 to 360
sorry helping others too

Answer 12

i know how to convert to radians

Answer 13

So first draw these two solutions we found as follows: