Radians Watch

e-n-i-g-m-a
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#1
Report Thread starter 13 years ago
#1
how do i find the exact value of cos 7/6pi without using a calculator... okay i know that by converting radians to degrees i get cos 210 ..but how do i solve this furthur ..
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mikeyT
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#2
Report 13 years ago
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You can either use a CAST diagram- I don't know how these work as I wasn't taught how to use one and I still can't figure it out.

Or use the symmetry of the graph of y=cos(x).
If you sketch the graph then you see that cos210= -cos30.

You should know cos30 from the triangle with hypotenuse (sp) 2 and sides of length 1 and √3.
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Malik
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(Original post by e-n-i-g-m-a)
how do i find the exact value of cos 7/6pi without using a calculator... okay i know that by converting radians to degrees i get cos 210 ..but how do i solve this furthur ..
note that 210=180+30

.:. cos(180+30)=cos210
....cos180cos30-sin180sin30 <== You should know these exact values
.....=-√3/2 - 0
.....=-√3/2
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Michael Scofield
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Report 13 years ago
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yup yup...what he said.

(1)Then -cos 30 can be further solved using the triangle.

(2)See attached file.

(3) Looking at the triangle, it is easy to see that -cos 30 is simply -(√3)/2

And that my friend, is your answer.


ATTN : This method will not work for all cases. In my opinion, you're better off learning the ASTC quadrant method. It makes life a lot easier.
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e-n-i-g-m-a
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#5
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I have learnt the ASTC method but how do i use that method in this case..??
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