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 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

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

Since

$\sec x = \frac{1}{\cos x}$

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

Harley

Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.