Given `tanalpha=5/(12)\ ` , find other trigonometric ratios

Explanation

We know that ,
`tan theta=("perpendicular")/("base")=(5)/(12)`
Now , constriuct a `DeltaPQR` in which
`PR=12k,QR=5kandangleQRP=90^(@)`.
Let`angleQPR=theta`
In `DeltaPQR`
From Pythagoras theorem
`PQ^(2)=PR^(2)+QR^(2)`
`rArr = (12k)^(2)+(5k)^(2)=144k^(2)+25k^(2)=16k^(2)`
`rArr PQ=13k`
Now ,
`sin theta=("perpendicular")/("hypotenuse")=(QR)/(PQ)=(5k)/(13k)=(5)/(13)`
`cos theta=("base")/("hypotenuse")=(PR)/(PQ)=(12k)/(13k)=(12)/(13)`
`"cosec" theta=("hypotenuse")/("perpendicular")=(PQ)/(QR)=(13k)/(5k)=(13)/(5)`
`sec theta=("hypotenuse")/("base")=(PQ)/(PR)=(13k)/(12k)=(13)/(12)`
`cot theta=("base")/("perpendicular")=(PR)/(QR)=(12k)/(5k)=(12)/(5)`