How do you calculate $tan(arccos(5/13))$ ?

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Answer 1 · 2015-02-06T14:50:39

The answer is: $12/5$ .

If you set $alpha=arccos(5/13)rArrcosalpha=5/13$ than we have to calculate:

$tanalpha=sinalpha/cosalpha$ .

$cosalpha=5/13rArrsinalpha=sqrt(1-cos^2alpha)=sqrt(1-25/169)=$

$=sqrt((169-25)/169)=sqrt(144/169)=12/13$ .

So:

$tanalpha=(12/13)/(5/13)=12/13*13/5=12/5$ .

How do you calculate tan(arccos(5/13))tan(arccos(5/13))?