# Mathematics Weblog

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## More Trig Ratios

Monday 23 May 2005 at 9:42 pm | In Articles | 6 CommentsStudents studying A level mathematics are expected to know exact values of a few trig ratios such as (see Trig Ratios posting). But a visit to Mathworld reveals a whole world of fascinating values.

Here are just a few of them (you may wish to try proving them)

where

where the sequence of signs repeats with period 3

As I said, fascinating!

Thank goodness can show these values easily!

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In re the first line: unless I’m missing some subtle joke, you want sin(45) to be sqrt(2)/2. Otherwise sin(45) is the same as sin(60), and this would make your unit circle lumpy.

Comment by Christian Claiborn — Tuesday 24 May 2005 4:16 pm #

Aaargh! How did that 4 get there? Corrected now. Thanks very much for pointing it out!

Comment by Steve — Tuesday 24 May 2005 5:38 pm #

Interesting note: you can use such results, together with the fact we know how to solve cubics/quartics explicitly, to prove that the sine of ONE degree (pi/180) is expressible as a radical!

Comment by Mr Blobby — Thursday 26 May 2005 12:21 am #

Why, I wonder, write (1/5)√(25+10√5)) rather than √(1+ 2/√5) ? … And why do my plus and minus signs vanish when I hit Preview?

Comment by Anton Sherwood — Tuesday 14 June 2005 5:44 am #

I have corrected the + sign bug, thanks for that

Comment by steve — Tuesday 14 June 2005 5:17 pm #

Well I did one exercise using complex numbers which helped me find the exact value of the cosine and sine of pi/12

with and

now

Comment by Luc — Friday 31 March 2006 5:53 pm #