Question

If `tanx=-2/9` `sinx>0`, how do you find the sin, cos, sec, csc, and cot?

Answer 1

If `tan(x)` is negative and `sin(x)` is positive,
`x` must be in Quadrant 2

and evaluation is only a matter of reading the graph.

Assuming `x epsilon [0,2pi]`

`sin(x) = 2/sqrt(85)`

#cos(x) = - 9/sqrt(85)

`csc(x) = sqrt(85)/2`

`sec(x) = -sqrt(85)/9`

`cot(x) = -9/2`