Question

How do you find the other trigonometric functions given `tantheta=2/3, sectheta=sqrt13/3`?

Answer 1

the other trigonometric functions are `sintheta=2/sqrt13`
`costheta=3/sqrt13` `cottheta=3/2` `cosectheta=sqrt13/2`

Explanation:

it is given that `sectheta=sqrt13/2rArrcostheta=3/sqrt13`
`tantheta=2/3` since `tantheta=sintheta/costhetarArr2/3=sintheta(sqrt13/3)`
`rArrsintheta=2/sqrt13` since `cosectheta=1/sinthetarArrcosectheta=sqrt13/2`
since `cottheta=1/tanthetarArrcottheta=3/2`