Question

How do you determine `tantheta` given `sintheta=-1/3, 180^circ<theta<270^circ`?

Answer 1

`tan(theta)=1/(2sqrt(2))`

Explanation:

If `180^@ < theta < 270^@`
and `sin(theta)=-1/3`
then

The adjacent side is calculated using the Pythagorean Theorem as
`-sqrt(3^2-1^2)=-2sqrt(2)`
Givin
`tan(theta)="opposite"/"adjacent"=((-1))/((-2sqrt(2)))= 1/(2sqrt(2)`