Question

Question #2daa7

Answer 1

`"see explanation"`

Explanation:

`costheta<0` indicating that `theta` could be in the second or third quadrants.

`•color(white)(x)sin^2theta+cos^2theta=1`

`rArrsintheta=+-sqrt(1-cos^2theta)`

`color(white)(rArrsintheta)=+-sqrt(1-(-1/2)^2)`

`color(white)(rArrsintheta)=+-sqrt(3/4)=+-sqrt3/2`

`•color(white)(x)tantheta=sintheta/costheta=+-(sqrt3/2)/(1/2)=+-sqrt3`

`•color(white)(x)cottheta=1/tantheta=+-1/sqrt3`

`•color(white)(x)sectheta=1/costheta=1/(-1/2)=-2`

`•color(white)(x)csctheta=1/sintheta=+-1/(sqrt3/2)=+-2/sqrt3`