Math CentralQuandaries & Queries


Question from Diana,

Please help me find the exact value of the following trigonometric expression:
sec(pi/12). Thanks!


Hi Diana,

I don't memorize many trig formulas but I do know

\[ \sin^2 x + \cos^2 x = 1\]

and the double angle formulas for the sine and cosine, in particuar

\[\cos 2x = \cos^2 x - \sin^2 x.\]

Substituting from the first equation into the second I get

\[\cos 2x = 1 + 2 \cos^2 x\]

and hence

\[\cos x = \sqrt{ \left( \frac{cos 2x - 1}{2} \right)} .\]


\[\sec x = \frac{1}{\cos x}\]

you can use the expression for the $\cos x$ above to determine the uantity you want if you know the cosine of $\large \frac{\pi}{6}.$


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