c3 helppp Watch

madhadiya
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#1
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#1
how would you solve 0<x<360

cos2x=1/3

thanks
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the bear
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#2
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how far have you got with this ?
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Imranfr0
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#3
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Is that C3 or C2? Anyway, to start, multiply the range by 2, so it becomes 0<2x<720
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crayolaguy
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#4
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(Original post by madhadiya)
how would you solve 0<x<360

cos2x=1/3

thanks
What have you got so far? and what can't you figure out?
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buxtonarmy
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C3? Isn't this C2?
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crayolaguy
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(Original post by buxtonarmy)
C3? Isn't this C2?
yeah, this is core 2. A core 3 question would be something like sec^2(2x) = 25 or something
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Toon800
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No, it's C3. You have to use the double angle rule as you have the Cos2X there.

Cos2X = 1-2Sin^2 X

So you have 1-2Sin^2 X = 1/3

Can you go from there? :P


If you can't:

Gather your like terms and simplify:

1 - 1/3 = 2Sin^2X --> 2/3 = 2Sin^2X

1/3 = Sin^2X

Then square root since Sin^x is actually (Sinx)^2

sqrt(1/3) = Sin X

X = Sin^-1(sqrt(1/3))

That solves for 35.26 degrees.

Then I find it's easiest to draw the graph of Sin (since you have that last bit of your previous workings as Sin)

And see where you have your other solution.
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crayolaguy
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(Original post by Toon800)
No, it's C3. You have to use the double angle rule as you have the Cos2X there.

Cos2X = 1-2Sin^2 X

So you have 1-2Sin^2 X = 1/3

Can you go from there? :P
Well this kind of question is in core 2 and 3...
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buxtonarmy
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#9
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You don't need the double angle formula though?

Can't you just make it 2X = cos-1 1/3 and solve from there?
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crayolaguy
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#10
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(Original post by Toon800)
No, it's C3. You have to use the double angle rule as you have the Cos2X there.

Cos2X = 1-2Sin^2 X

So you have 1-2Sin^2 X = 1/3

Can you go from there? :P
Don't you think you're over complicating things a bit...

you just multiply your range by 2 so... 0 < 2x < 720
then cos^-1(1/3) = x
find all of the x values by looking at the cos graph from 0 to 720
divide them all by 2
done
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Imranfr0
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#11
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#11
(Original post by Toon800)
No, it's C3. You have to use the double angle rule as you have the Cos2X there.

Cos2X = 1-2Sin^2 X

So you have 1-2Sin^2 X = 1/3

Can you go from there? :P
I thought that you could just solve it by doing 2x=cos-11/3 and then when you got the result, divide it by 2 and add/take away 180o​... lol
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buxtonarmy
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(Original post by Imranfr0)
I thought that you could just solve it by doing 2x=cos-11/3 and then when you got the result, divide it by 2 and add/take away 180o​... lol
Yeah lol that's what I thought??
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Imranfr0
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(Original post by buxtonarmy)
Yeah lol that's what I thought??
Same, using the double angle formula makes it more complicated than it is xD
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Toon800
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(Original post by Imranfr0)
Same, using the double angle formula makes it more complicated than it is xD
Yep, it's just the C3 way so that's how I solved the equation :P
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Imranfr0
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#15
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(Original post by Toon800)
Yep, it's just the C3 way so that's how I solved the equation :P
I see
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totoro1997
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#16
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#16
Hi, I know this is unrelated to trigonometry but can I have some help on this c3 question please?
The part of the graph between y=e^1/2x, the line y=x and the y axis is rotated about the x axis to make a solid of revolution. Find the
volume of this solid, giving your answer in the form of pi (alnb-c), where a, b and c are integers.
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totoro1997
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#17
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#17
Hi, I know this is unrelated to trigonometry but can I have some help on this c3 question please?
The part of the graph between y=e^1/2x, the line y=2 and the y axis is rotated about the x axis to make a solid of revolution. Find the
volume of this solid, giving your answer in the form of pi (alnb-c), where a, b and c are integers.
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madhadiya
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#18
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#18
(Original post by Toon800)
No, it's C3. You have to use the double angle rule as you have the Cos2X there.

Cos2X = 1-2Sin^2 X

So you have 1-2Sin^2 X = 1/3

Can you go from there? :P


If you can't:

Gather your like terms and simplify:

1 - 1/3 = 2Sin^2X --> 2/3 = 2Sin^2X

1/3 = Sin^2X

Then square root since Sin^x is actually (Sinx)^2

sqrt(1/3) = Sin X

X = Sin^-1(sqrt(1/3))

That solves for 35.26 degrees.

Then I find it's easiest to draw the graph of Sin (since you have that last bit of your previous workings as Sin)

And see where you have your other solution.
Thanks I got up till x=35.3 and x=324.7, but apparently there should be 4 answers??
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totoro1997
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#19
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#19
When you square root 1/3 the answer could be positive or negative (I think)
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