Question

Question #153fd

Answer 1

From the above figure

Given the coordinates of point Q (3,-9)
`ON=3 and QN=-9`

`OQ=sqrt(ON^2+QN^2)`

Now

`sintheta="opposite"/"hypotenuse"=(QN)/(OQ)=-9/(3sqrt10)=-3/sqrt10`

So `csctheta=1/sintheta=-sqrt10/3`

`costheta="adjacent"/"hypotenuse"=(ON)/(OQ)=3/(3sqrt10)=1/sqrt10`

So `sectheta=1/costheta=sqrt10`

`tantheta="opposite"/"adajcent"=(QN)/(ON)=-9/3=-3`

So `cottheta=1/tantheta=-1/3`