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# Help with AS Maths question (CAST) watch

1. Hi can someone help me with this CAST Diagram question? I’m having trouble understanding how to find the 2nd, 3rd and 4th values- like why we have to subtract 360 to get some of them etc
Question: ‘Solve tan2x= square root of 3 at interval -180°<x<180°
Thanks!
2. Honestly I don't bother with the CAST diagram. Instead you can just draw yourself a little sketch of the tan graph. Let's say you got a value of 45o which is tan^-1(1), right? Draw a line across the y axis at the value of 1. This horizontal line on the graph will hit the lines on the tan graph where it =1, you can then read off of the points of intersection to get your values in degrees (on x axis). So let's say you've worked out your first value as 45o, when you draw a line at y=1, you'll see that it crosses at another point in the negative numbers. The tan graph repeats itself every 180o, right? So just take 180 away from 45o to get the other (negative) value. Hope this helps, sorry it's difficult to explain/ understand, but look at a tan graph while you read this haha n hopefully it makes sense ) this also works for cos and sin
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3. (Original post by LilN)
Honestly I don't bother with the CAST diagram. Instead you can just draw yourself a little sketch of the tan graph. Let's say you got a value of 45o which is tan^-1(1), right? Draw a line across the y axis at the value of 1. This horizontal line on the graph will hit the lines on the tan graph where it =1, you can then read off of the points of intersection to get your values in degrees (on x axis). So let's say you've worked out your first value as 45o, when you draw a line at y=1, you'll see that it crosses at another point in the negative numbers. The tan graph repeats itself every 180o, right? So just take 180 away from 45o to get the other (negative) value. Hope this helps, sorry it's difficult to explain/ understand, but look at a tan graph while you read this haha n hopefully it makes sense ) this also works for cos and sin
I also find it easier with the graph, I know it's not easy to describe in words though.
4. Question: ‘Solve tan2x= square root of 3 at interval -180°<x<180°

To make it easier to understand:

-180<x<180 --> -360<2x<360

tan 2x = root 3
Principal value of 2x = 60.

Drawing CAST helps you to realise that 2x = 60, 240,-120, -300.

So x = ...
5. We'll need to accommodate the 2x here, with an easier method.

What we can do here is do a regular graph (of tanx) (perhaps on your graphical calculator), on Desmos, but instead of going from -180<x<180, we're going to double the period, so -360<x<360.

We can then find all of our roots from here, once you have them, you can divide through by 2 to get your tan2x roots, but, please be aware, if any of your divide results fall within outside of the range (i.e above 180 or below -180), you'll have to omit them.
6. Brilliant thanks everyone!!
7. the simplest way to under this drawing quadrants. do u know about it?
(Original post by geometric)
Hi can someone help me with this CAST Diagram question? I’m having trouble understanding how to find the 2nd, 3rd and 4th values- like why we have to subtract 360 to get some of them etc
Question: ‘Solve tan2x= square root of 3 at interval -180°<x<180°
Thanks!
Posted on the TSR App. Download from Apple or Google Play

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