Question

How do you find the remaining trigonometric functions of `theta` given `costheta=sqrt3/2` and `theta` terminates in QIV?

Answer 1

`"see explanation"`

Explanation:

`"since "theta" is in quadrant 4 then apart from"`

`costheta" and "sectheta" all other trig. ratios are negative"`

`•color(white)(x)costheta=sqrt3/2`

`•color(white)(x)sectheta=1/costheta=2/sqrt3=(2sqrt3)/3`

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

`color(white)(xxxxx)=-sqrt(1-3/4)=-1/2`

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

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

`•color(white)(x)cottheta=1/tantheta=-sqrt3/3`