Question

How do you find the five remaining trigonometric function satisfying `costheta=-2/5`, `sintheta>0`?

Answer 1

`sin theta= sqrt 21/5 , csc theta=5/sqrt 21 ,tan theta= - sqrt 21/2`
`cot theta= -2/sqrt 21 , sec theta=-5/2`

Explanation:

In right triangle `cos theta = a/h =-2 /5 :.a=-2 , h=5`

`:.o=sqrt(5^2-2^2)= sqrt 21 ; a,,o, h` are adjacent side, opposite

side and hypotenuse. `sin theta= o/h= sqrt 21/5` ,

`tan theta= o/a= - sqrt 21/2, csc theta= h/o= 5/sqrt 21` ,

`sec theta= h/a= - 5/2, cot theta= a/o= -2/sqrt 21` [Ans]