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C2 Trig Question

Hi, I was doing the MEI C2 2005 paper and I'm confused about question 3):

It says 'solve the equation sinx = -0.2 between 0 and 360.

I assumed you'd take sin-1(-0.2) which is 11.54, and then using CAST the values of the two solutions would be 11.54 and then 180-11.54 which is 168.46. However these were not the correct answers - what did I do wrong?
(edited 8 years ago)
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Reply 1
Avatar for TeeEm
TeeEm
19
Original post by Avacado
Hi, I was doing the MEI C2 2005 paper and I'm confused about question 3):

It says 'solve the equation sinx = -0.2 between 0 and 360.

I assumed you'd take sin-1(-0.2) which is 11.54, and then using CAST the values of the two solutions would be 11.54 and then 180-11.54 which is 168.46. However these were not the correct answers - what did I do wrong?


180 - (-11.54)
Reply 2
Avatar for RMNDK
RMNDK
3
Original post by Avacado
Hi, I was doing the MEI C2 2005 paper and I'm confused about question 3):

It says 'solve the equation sinx = -0.2 between 0 and 360.

I assumed you'd take sin-1(-0.2) which is 11.54, and then using CAST the values of the two solutions would be 11.54 and then 180-11.54 which is 168.46. However these were not the correct answers - what did I do wrong?


sin-1 (-0.2) ≠ 11.54

It might be helpful to look at the graph you've drawn in part a.
Plot a straight line at -0.2 and look at where the line cuts the graph.
You'll see that one of the solutions is above 180.
Sin-1(-0.2) = -11.54 not 11.54 so other solutions are 180--11.54 =191.54 and360+-11.54=348.46
And yeah I just use the graph I think casts not a great method
Reply 5
Avatar for Avacado
Avacado
OP
2
Oh! I'm not sure why it got a positive value... I must have misread, I have a habit of doing so :frown:

Thank you - personally I find CAST easier to use assuming I can actually get the signs the right way around, it just seems quicker than using the graph.
Reply 6
Avatar for RMNDK
RMNDK
3
Original post by Avacado
Oh! I'm not sure why it got a positive value... I must have misread, I have a habit of doing so :frown:

Thank you - personally I find CAST easier to use assuming I can actually get the signs the right way around, it just seems quicker than using the graph.


I fully agree.
CAST makes everything so much easier because it's all on one graph, and it makes those pesky equations like sin(2x) or cos(3x-60) easier to deal with
Original post by RMNDK
I fully agree.
CAST makes everything so much easier because it's all on one graph, and it makes those pesky equations like sin(2x) or cos(3x-60) easier to deal with


well some things like sinx=0 it's easier to use the graph IMO
Reply 8
Avatar for RMNDK
RMNDK
3
Original post by thefatone
well some things like sinx=0 it's easier to use the graph IMO


Surely with sinx = 0 you don't even need the graph or CAST for that matter? I mean, it's quite standard to know the intervals along the x-axis for each appropriate trigonometric graph..
But I see where you're coming from. I do appreciate the visual aspect and the symmetry idea is helpful.
Original post by RMNDK
Surely with sinx = 0 you don't even need the graph or CAST for that matter? I mean, it's quite standard to know the intervals along the x-axis for each appropriate trigonometric graph..
But I see where you're coming from. I do appreciate the visual aspect and the symmetry idea is helpful.


fairs tbh i know the intervals aswell xD it's easy to learn, sometimes though i just draw a sine or cosine graph to check how many values i should have since sometimes i get the wrong number of results.
Reply 10
Avatar for RMNDK
RMNDK
3
Original post by thefatone
fairs tbh i know the intervals aswell xD it's easy to learn, sometimes though i just draw a sine or cosine graph to check how many values i should have since sometimes i get the wrong number of results.


I definitely agree with that point; its the main reason why even after doing a question using CAST, I'll still draw a little diagram with any appropriate transformation to see how many solutions there are.
That's a problem with CAST, you just keep going round and round and you can often lose track.
I think cast is probably easier however I think it's easier to understand how trigonometry actually works with using the graph

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