If tan θ = (-4/3), then sin θ is

Question

If tan θ = (-4/3), then sin θ is (A) (-4/5) but not (4/5) (B) (-4/5) or (4/5) (C) (4/5) but not - (4/5) (D) None of these

Tardigrade Admin · Accepted Answer

Since tan θ = - (4/3) is negative, θ lies either in second quadrant or in fourth quadrant . Thus sin θ = (4/5) if θ lies in the second quadrant or sin θ = - (4/5) if θ lies in the fourth quadrant.

Q. If $tan θ = \frac{- 4}{3}$ , then $sin θ$ is

$\frac{- 4}{5}$ but not $\frac{4}{5}$

$\frac{- 4}{5}$ or $\frac{4}{5}$

$\frac{4}{5}$ but not $- \frac{4}{5}$

None of these

Since $tan θ = - \frac{4}{3}$ is negative, $θ$ lies either in second quadrant or in fourth quadrant .
Thus $sin θ = \frac{4}{5}$ if $θ$ lies in the second quadrant
or $sin θ = - \frac{4}{5}$ if $θ$ lies in the fourth quadrant.

Q. If tanθ=3−4​, then sinθ is

5−4​ but not 54​

5−4​ or 54​

54​ but not −54​