Question

If the terminal arm passes through the point (1,$-$1) making an angle $\theta$, find the value of sec$\theta$.

Answer 1

The terminal arm lies in quadrant IV.
$$\begin{gathered} \mathrm{In}△OAB,\mathrm{we}\mathrm{have}: \\ \tan \theta =\frac{BA}{OA}=\frac{-1}{1} \\ \Rightarrow \tan \theta =-1 \\ \Rightarrow \tan \theta =-\tan 45° \\ \Rightarrow \theta =\left(-45°\right)(\because \theta \mathrm{lies}\mathrm{in}\mathrm{quadrant}\mathrm{IV}) \\ \mathrm{Then}\sec \theta =\sec \left(-45°\right) \\ =\sec \left(45°\right)=\sqrt{2} \end{gathered}$$