Question

if sin =-2/5 and tan <0 find the exact value of the other trigonometric functions ?

Answer 1

`sinA=-2/5`, `cosA=sqrt21/5`, `tanA=-2/sqrt21`
`cotA=-sqrt21/2`, `secA=5/sqrt21` and `cscA=-5/2`

Explanation:

As `sinA=-2/5` and `tanA < 0` (note that it means `cotA < 0`,

we have `cscA=-5/2` and as `csc^2A=cot^2A+1`

i.e. `cot^2A=csc^2A-1=(-5/2)^2-1=25/4-1=21/4`

and `cotA=-sqrt21/2` (as it is negative) and `tanA=-2/sqrt21`

Hence `cosA=sinA/tanA=(-2/5)/(-2/sqrt21)=sqrt21/5`

and `secA=5/sqrt21`