Question

If `tantheta>0` and `csctheta=2`, find all the trigonometrical ratios of `theta`?

Answer 1

`sintheta=1/2`, `csctheta=2`, `costheta=sqrt3/2`, `sectheta=2/sqrt3`, `tantheta=1/sqrt3` and `cottheta=sqrt3`

Explanation:

`tantheta > 0` mean `theta` is either in `Q1` or in `Q3`

As `csc theta = 2`, `theta` is in `Q1` only.

As `csctheta=2`, `sin theta = 1/2 = sin 30^@`

Hence `theta = 30 ^@`

So,
`cos 30^@ = sqrt3/2, sec 30^@ = 2/sqrt3, tan 30^@ = 1/sqrt3 = 0.57" which is greater than " 0, cot 30^@ = sqrt3, sin 30^@ = 1/2 and csc 30^@ = 2`