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GH
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#1
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#1
I'm rather stuck on this question.

given that cosec C = 7, sin²D = 0.5 and tan²E = 4, find the possible values of cot C, sec D and cosec E, giving your answers in exact form.

*******************************


I started by doing:

cosec C = 7

1/(sin C) = 7

(1/7) = sin C

But then got stuck about here.
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username9816
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#2
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(Original post by 2776)
I'm rather stuck on this question.

given that cosec C = 7, sin²D = 0.5 and tan²E = 4, find the possible values of cot C, sec D and cosec E, giving your answers in exact form.

*******************************


I started by doing:

cosec C = 7

1/(sin C) = 7

(1/7) = sin C

But then got stuck about here.
Poor 2776, nobody has helped him on his maths question yet.
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What's Chico Time Precious?
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:confused: Do you do edexcel p3? not seen anything like that before sorry.
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GH
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(Original post by Absolution)
:confused: Do you do edexcel p3? not seen anything like that before sorry.
OCR
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What's Chico Time Precious?
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(Original post by 2776)
OCR
ah that would explain it, i haven't covered that sort of equation before and hopefully won't have too good luck !
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JamesF
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#6
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1 + cot^2 = cosec^2, so
cot^2 C = 48 etc
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IntegralAnomaly
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(Original post by 2776)
I'm rather stuck on this question.

given that cosec C = 7, sin²D = 0.5 and tan²E = 4, find the possible values of cot C, sec D and cosec E, giving your answers in exact form.

*******************************


I started by doing:

cosec C = 7

1/(sin C) = 7

(1/7) = sin C

But then got stuck about here.
i got cot C=sqrt(48),sec D=sqrt(2) and -sqrt(2),cosec E=sqrt(5)/2.
There are more asumming postive and negative roots,also wot are the domains of the angles C, D, E?
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GH
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(Original post by IntegralAnomaly)
i got cot C=sqrt(48),sec D=sqrt(2) and -sqrt(2),cosec E=sqrt(5)/2.
There are more asumming postive and negative roots,also wot are the domains of the angles C, D, E?
No domains mentioned. I think it is only wanting to ask for the first few answers. Cheers, got it now.
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hornblower
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#9
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(Original post by 2776)
I'm rather stuck on this question.

given that cosec C = 7, sin²D = 0.5 and tan²E = 4, find the possible values of cot C, sec D and cosec E, giving your answers in exact form.
cosec C = 7

squaring gives:

cosec^2 C = 49

using identity gives:

1 + cot^2 C = 49

rearranging gives:

cot^2 C = 48

square rooting gives:

cot C = plus or minus √48 = plus or minus 4√3


sin^2 D = 0.5

using identity gives:

1 - cos^2 D = 0.5

rearranging gives:

cos^2 D = 0.5

square rooting gives

cos D = plus or minus 1/√2

taking reciprocal:

sec D = plus or minus √2


I'll have to think about the third one.
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GH
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#10
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its really the E one taht I'm stuck on, tried sec²E = 5, then sin²E/cos²E = 4, but not really going anywhere.
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IntegralAnomaly
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#11
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(Original post by hornblower)
cosec C = 7

squaring gives:

cosec^2 C = 49

using identity gives:

1 + cot^2 C = 49

rearranging gives:

cot^2 C = 48

square rooting gives:

cot C = plus or minus √48 = plus or minus 4√3


sin^2 D = 0.5

using identity gives:

1 - cos^2 D = 0.5

rearranging gives:

cos^2 D = 0.5

square rooting gives

cos D = plus or minus 1/√2

taking reciprocal:

sec D = plus or minus √2


I'll have to think about the third one.
for the third 1 tanE=2(im nt taking the negative 1)
therefore sinE=2/(sqrt(5)) (using a right angled triangle with angle E)
ergo cosec E =sqrt(5)/2
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Ben.S.
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#12
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#12
(Original post by 2776)
I'm rather stuck on this question.

given that cosec C = 7, sin²D = 0.5 and tan²E = 4, find the possible values of cot C, sec D and cosec E, giving your answers in exact form.

*******************************


I started by doing:

cosec C = 7

1/(sin C) = 7

(1/7) = sin C

But then got stuck about here.
For cosec(E), if you take the reciprocal of tan^2(E) to find cot^2(E) = 1/4, then use the identity;

cosec^2(E) = 1 + cot^2(E)

So cosec^2(E) = 5/4 and cosec(E) = (sqrt5)/2, as the person above correctly stated.

Ben
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IntegralAnomaly
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#13
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#13
(Original post by Ben.S.)
For cosec(E), if you take the reciprocal of tan^2(E) to find cot^2(E) = 1/4, then use the identity;

cosec^2(E) = 1 + cot^2(E)

So cosec^2(E) = 5/4 and cosec(E) = (sqrt5)/2, as the person above correctly stated.

Ben
oh yes thats a much better way
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