Question

If `cotA=5/12` and A lies in 3rd quadrant, then find the values of five other trignometric ratios.

Answer 1

`cotA = 5/12`
`rArr tanA=1/(cotA) = 12/15`.
Now, `"cosec^(2)A=1+cot^(2)A`
`=1+(5/12)^(2)=169/144`
`rArr "cosec"A = -13/12`
`therefore` cosecA is negative in 3rd quadrant
sinA`=1/("cosec"A)=-12/13`
`cosA=(cosA)/(sinA).sinA`
`=cotA. sinA`
`=5/12(-12/13)=-5/13`
`secA=1/(cosA)=-13/5`