You are Here: Home

# C2: Alternatives to CAST Diagram

Maths and statistics discussion, revision, exam and homework help.

Announcements Posted on
Find out how cards are replacing warnings on TSR...read more 03-12-2013
1. C2: Alternatives to CAST Diagram
Alright so I've been taught this 'CAST' diagram although in some situations it may get confusing (here and there).

My point is, within an 07 paper there was a question asking to sketch trig graphs - now how are you suppose to do that from the 'CAST diagram'? (I wasn't taught it, although then again my fault for only finding out now and not earlier)

And as for solving trig equations, are their any specific rules as an alternative? I'm not quite fond on using this method.
2. Re: C2: Alternatives to CAST Diagram
I never really did CAST diagrams, so I'll show you how the trig graphs look:

http://cosketch.com/Saved/pPsS9r4o

For sin(x), start with the curve going up and down from 0 to 360, with the y values between -1 and 1. Then this shape repeats every 360 degrees. That's the bit you need to remember. Then, you can work out that the curve crosses the x axis at 180 (this is half of 360) and has maximum/minimum points at 90 and 270.

For cos(x), you have a different shape - it's sometimes known as the 'cosine bucket' to help you distinguish it. This also repeats every 360 degrees.

To solve trig equations using it, that's a bit harder. You might find it easier to carry on using CAST diagrams rather than learn a whole new method.

You might solve a trig equation and end up with, say, sin(x)=1/4, for -180<x<180. You would then sketch the y=sin(x) graph for that range, and put in a horizontal line at y=1/4:

http://cosketch.com/Saved/pw6twqm0

You see that the solutions for x are a and b. You can calculate a by doing sin^-1(1/4). To get b, look at the shape of the curve between x=0 and x=a, then look at the shape between x=b and x=180. Notice that the shape is the same, apart from a reflection (and my bad drawing). So this means that the distance from 0 to a is the same as the distance from b to 180. Therefore, b=180-a.

If you're interested in taking this approach then you would probably want to try lots of questions on this, since depending on the solutions/ranges involved you would have to take different approaches when it comes to recognising the shape of the graph to get the different solutions.
3. Re: C2: Alternatives to CAST Diagram
CAST or ASTC (All Stations To Central, as I learnt it :P) is sorta more useful for quickly demonstrating to the marker that you understand which quadrant a particular trigonometric function should be in. It's somewhat quicker and less ambiguous than just drawing a sine or cosine curve, for example. In your mind, you can use either CAST or the actual curves, it doesn't matter, but on paper, CAST is clearer.

## Step 2: Register

Thanks for posting! You just need to create an account in order to submit the post
1. this can't be left blank

this is what you'll be called on TSR

2. this can't be left blank

never shared and never spammed

3. this can't be left blank

6 characters or longer with both numbers and letters is safer

4. this can't be left empty
1. By completing the slider below you agree to The Student Room's terms & conditions and site rules

2. Slide the button to the right to create your account

You don't slide that way? No problem.

Last updated: May 6, 2012
Study resources