If `sec theta = (5)/(3) and 0 lt theta lt (pi)/(2)`. Find all the other T-ratios.

Answer

`sin theta = (4)/(5), " "cos theta= (3)/(5), " "tantheta= (4)/(3)`,
`cot theta= (3)/(4)," "cosestheta= (5)/(4)`

Explanation

`sec theta = (5)/(3)`

we know that, `sec theta = (H)/( B) = (5)/(3) `
`cos theta = (3)/(5)` ,
we know 3, 4, 5 are phthogorous triplets
`therefore P=4`
i.e. `" "H: B : P = 5 : 3: 4`
`therefore sin theta = (4)/(5) " "cosect theta = (5)/(4)`
`" "cos theta = (3)/(5) " "sec theta = (5)/(3)`
`" "tan theta = (4)/(3) " "cot theta = (3)/(4)`