Question

Question #c6847

Answer 1

`"see explanation"`

Explanation:

`"given "csctheta=3" then"`

`•color(white)(x)sintheta=1/csctheta=1/3`

`"since "sintheta>0" this indicates that "theta` is in the first or second quadrant.

`•color(white)(x)costheta=+-sqrt(1-sin^2theta)`

`color(white)(xxxxxx)=-sqrt(1-1/9)=-sqrt(8/9)`

`color(white)(xxxxxx)=-(2sqrt2)/3`

`•color(white)(x)sectheta=1/costheta=-1/((2sqrt2)/3)=-3/(2sqrt2)=-(3sqrt2)/4`

`•color(white)(x)tantheta=sintheta/costheta=(1/3)/(-(2sqrt2)/3)=-1/(2sqrt2)=-sqrt2/4`

`•color(white)(x)cottheta=1/tantheta=1/(-sqrt2/4)=-4/sqrt2=-2sqrt2`

`theta" is in the second quadrant"`