evaluate cos(2 tan^-1(1/3))

I figure if I can evaluate arctan of 1/3 I can solve it (multiply by two and take the cosine of the result).

Is it advisable to do this with a calculator or is the value of acrtan(1/3) commonly known value?

thanks!

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- Oct 16th 2012, 12:40 PMkingsolomonsgraveevaluating inverse trig functions
evaluate cos(2 tan^-1(1/3))

I figure if I can evaluate arctan of 1/3 I can solve it (multiply by two and take the cosine of the result).

Is it advisable to do this with a calculator or is the value of acrtan(1/3) commonly known value?

thanks! - Oct 16th 2012, 01:13 PMSorobanRe: evaluating inverse trig functions
Hello, kingsolomonsgrave!

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- Oct 16th 2012, 01:21 PMTheEmptySetRe: evaluating inverse trig functions
You don't need to know the value. Remember that inverse trig functions are angles!

Let

So by the double angle identity we have

Now we just need to figure out

So we can draw a triangle and use the pythagorean theorem

Attachment 25253

This shows that

Now just plug this in to finish..