Question

How do you find the remaining trigonometric functions of `theta` given `sectheta-=13/5` and `sintheta<0`?

Answer 1

`"see explanation"`

Explanation:

`"since "sintheta<0" this indicates that "theta" is in the"`
`"the third or fourth quadrants"`

`•color(white)(x)costheta=1/sectheta=1/(13/5)=5/13`

`•color(white)(x)sintheta=+-sqrt(1-cos^2theta)`

`rArrsintheta=-sqrt(1-(5/13)^2)`

`color(white)(rArrsintheta)=-sqrt(144/169)=-12/13`

`•color(white)(x)csctheta=1/sintheta=1/(-12/13)=-13/12`

`•color(white)(x)tantheta=sintheta/costheta=(-12/13)/(5/13)=-12/5`

`•color(white)(x)cottheta=1/tantheta=1/(-12/5)=-5/12`

`theta" is in the fourth quadrant"`