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quick question, CAST diagram

Hey,

I can't get my head around how they've solved this using the CAST diagram.

cos x = −sqrt32-\frac {sqrt 3}{2}

and x = 150

so in the mark scheme it says clockwise rotation of 150 or anti-clockwise rotation of 210

can someone explain this for me please?
Reply 1
Avatar for Zacken
Zacken
22
Original post by Ravster
Hey,

I can't get my head around how they've solved this using the CAST diagram.

cos x = −sqrt32-\frac {sqrt 3}{2}

and x = 150

so in the mark scheme it says clockwise rotation of 150 or anti-clockwise rotation of 210

can someone explain this for me please?


I'm not sure what you mean? There are two solutions, one where x=150∘x=150^{\circ} and one where x=360∘−150∘=210∘x = 360^{\circ} - 150^{\circ} = 210^{\circ}?
Reply 2
Avatar for Ravster
Ravster
OP
12
Original post by Zacken
I'm not sure what you mean? There are two solutions, one where x=150∘x=150^{\circ} and one where x=360∘−150∘=210∘x = 360^{\circ} - 150^{\circ} = 210^{\circ}?


Thanks for your reply and help.

The bit where they got 360-150 to get 210. Why did you do this?
Original post by Ravster
Thanks for your reply and help.

The bit where they got 360-150 to get 210. Why did you do this?


For Cos:
If the first solution is say x(degrees) then the second solution is always 360 (degrees)-x.

(Then the other solutions (if needed) are ±360 degrees the main 2 solutions above.)
Reply 4
Avatar for Zacken
Zacken
22
The reason the above is true is that cos⁡x=cos⁡(2π−x)\cos x = \cos (2\pi - x) which is fairly obvious from the graph, but I'm not very familiar with the CAST stuff.

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