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# Maths as level watch

1. Hi can someone help me with this CAST diagram question? I’m having trouble understanding how to work it out because there’s a lot of seemingly random subtraction and addition involved :0
‘Solve, in the interval -180°<theta<180°, tan2theta=square root of 3’
2. (Original post by geometric)
Hi can someone help me with this CAST diagram question? I’m having trouble understanding how to work it out because there’s a lot of seemingly random subtraction and addition involved :0
‘Solve, in the interval -180°<theta<180°, tan2theta=square root of 3’
Like I know the basics I’m just so confused when it comes to the two tan graphs and the fact that I have to minus 360 after getting 240° and so forth.
3. (Original post by geometric)
Hi can someone help me with this CAST diagram question? I’m having trouble understanding how to work it out because there’s a lot of seemingly random subtraction and addition involved :0
‘Solve, in the interval -180°<theta<180°, tan2theta=square root of 3’
The CAST diagram is supposed to help you make sense of the seemingly random calculations you need to do fpto find all of the valid solutions to a trig equation over a defined interval. If it's not helping, ask your teacher to explain it again. I'll try to link you to a video later.

Edit: video here, it takes a while to explain it but hopefully if you invest the time it will no longer be random calculations.

You may find it easier to sketch graphs of trig functions in order to identify where other solutions are to be found and what calculation is required to find them.
For example, a sketch of tan(theta) 0-360 will show you that the tan graph repeats every 180 degrees. Once you have the first solution from your calculator you can find other valid solutions by adding or subtracting multiples of 180.
4. (Original post by geometric)
Hi can someone help me with this CAST diagram question? I’m having trouble understanding how to work it out because there’s a lot of seemingly random subtraction and addition involved :0
‘Solve, in the interval -180°<theta<180°, tan2theta=square root of 3’
so it works like a normal cast question but instead of theta you have 2theta. first work the equation out like a normal cast diagram to find the principal angle for 2theta then find ALL the possible values for -360 to 360 (double the range because you're using 2theta in cast not theta). finally divide all those angles by 2 to find theta by itself.

hope that helps! if you're still stuck just let me know.

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Updated: February 23, 2018
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