Question

If tanθ = -1/2, find sinθ?

Answer 1

`sintheta=+-1/sqrt5`

Explanation:

`tantheta<0"`

`rArrtheta" lies in second or fourth quadrant"`

`sintheta>0" in second quadrant"`

`sintheta<0" in fourth quadrant"`

`"the final result must reflect this, that is "+-`

`"using the "color(blue)"trigonometric identities"`

`•color(white)(x)cottheta=1/tantheta" and "sintheta=1/csctheta"`

`•color(white)(x)csc^2theta=1+cot^2theta`

`cottheta=1/tantheta=1/(-1/2)=-2`

`rArrcsctheta=+-sqrt(1+(-2)^2)=+-sqrt5`

`rArrsintheta=+-1/sqrt5`