# Trigonometric equation help

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Thread starter 1 month ago
#1
Q: Solve for θ, in the interval -180° ≤ θ ≤ 180°
cosθ(cosθ - 2) = 1

I looked at solution banks https://activeteach-prod.resource.pe...b_p1_ex10f.pdf
(2c) and don't know how they got -114 using the cast diagram.

EDIT: I realise what I did to get it wrong. I needed an acute angle to use the cast diagram. So I did 180 - 114 and then used that angle. It gave me the correcrt answers but that was a extra weird step.
Last edited by GogetaORvegito?; 1 month ago
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1 month ago
#2
Expand, make it equal to 0
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1 month ago
#3
If it goes through -180, it has to be -114 too as that’s the interval
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Thread starter 1 month ago
#4
(Original post by Tracheostenosis)
Expand, make it equal to 0
Oh no I should've clarified in my op. I got that it is 1-√2 just like they did. I'm just confused how they show they got -114 using the cast diagram.
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1 month ago
#5
If you draw the Cos graph, it crosses at the negatives too, if you can try not to use the CAST diagram
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Thread starter 1 month ago
#6
(Original post by Tracheostenosis)
If you draw the Cos graph, it crosses at the negatives too, if you can try not to use the CAST diagram
Alright it looks a bit tricky I guess.
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1 month ago
#7
How? Most of year 2 trig you need to know how to draw it anyways so best to start practicing now
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Thread starter 1 month ago
#8
(Original post by Tracheostenosis)
How? Most of year 2 trig you need to know how to draw it anyways so best to start practicing now
No I mean it trickier using the cast diagram
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1 month ago
#9
Nah it isn’t tricky, it’s just not a healthy way to do trig imo
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Thread starter 1 month ago
#10
(Original post by Tracheostenosis)
Nah it isn’t tricky, it’s just not a healthy way to do trig imo
Wait so do you know how to represent -114 on the cast diagram? Cos I just want to know how that looks...
Last edited by GogetaORvegito?; 1 month ago
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1 month ago
#11
(Original post by GogetaORvegito?)
Wait so do you know how to represent -114 on the cast diagram? Cos I just want to know how that looks...
Personally I haven’t used the Cast diagram ever to do trig, but from what I can remember isn’t it like All students take calculus? And like the one which it lands on ? No idea lmao the diagram isn’t healthy, best way to handle trig questions in general is to draw the actual graphs
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Thread starter 1 month ago
#12
(Original post by Tracheostenosis)
Personally I haven’t used the Cast diagram ever to do trig, but from what I can remember isn’t it like All students take calculus? And like the one which it lands on ? No idea lmao the diagram isn’t healthy, best way to handle trig questions in general is to draw the actual graphs
Alright fine. I use All Students Try Crack lol. But yeah i'm just stuck cos if the range starts from -180 do I start from that position and end at 180 but then it says they looked at the 2nd at third quadrant which wouldn't make sense unless you just add the minus sign on the 180 cos your going the other way around but then it still doesn't give me -114 becasue if I add or takeaway from -180 it does not give me that.

But yeah I'm gonna drop this method, it will benefit me drawing the graphs so I can remember their shapes better. Thanks anyways
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1 month ago
#13
Lmao your acronym 😂😂😂😂😂

Yeah I’d definitely practice how to draw the actual graphs, you can see the points and exactly how many values you need. Especially when you’re working in Radians
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Thread starter 1 month ago
#14
(Original post by Tracheostenosis)
Lmao your acronym 😂😂😂😂😂

Yeah I’d definitely practice how to draw the actual graphs, you can see the points and exactly how many values you need. Especially when you’re working in Radians
I realize what I did to get it wrong. I needed an acute angle to use the cast diagram. So I did 180 - 114 and then used that angle. It gave me the correct answers but that was an extra weird step. Did I just find another disadvantage to this system lol. Why would you even need to represent it using the cast diagram at that point. This method is shambles
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1 month ago
#15
Lol it’s good to kinda understand it but after that drop it.
There’s graphs you need to know how to draw back to front in year 13, also radians too and the equivalent. It’s nothing like the CAST method 😂😂
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Thread starter 1 month ago
#16
(Original post by Tracheostenosis)
Lol it’s good to kinda understand it but after that drop it.
There’s graphs you need to know how to draw back to front in year 13, also radians too and the equivalent. It’s nothing like the CAST method 😂😂
Yes whoever made this method just wasted a page of paper in my text book. There is no way you can justify using this method now that I discovered what I found. Have a splendid day stranger
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1 month ago
#17
Lol you too stranger💀
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